Showing papers in "Israel Journal of Mathematics in 1987"
TL;DR: In this paper, an inequality bounding the growth rate of the volumes of iterates of smooth submanifolds in terms of the topological entropy was proved, which implies the entropy conjecture.
Abstract: An inequality is proved, bounding the growth rates of the volumes of iterates of smooth submanifolds in terms of the topological entropy. ForC
x-smooth mappings this inequality implies the entropy conjecture, and, together with the opposite inequality, obtained by S. Newhouse, proves the coincidence of the growth rate of volumes and the topological entropy, as well as the upper semicontinuity of the entropy.
584 citations
TL;DR: In this paper, the main problem of restricted invertibility of linear operators acting on finite dimensionallp-spaces is investigated, and the results obtained below enable us to complete earlier work on the structure of complemented subspaces of lp-space which have extremal euclidean distance.
Abstract: The main problem investigated in this paper is that of restricted invertibility of linear operators acting on finite dimensionallp-spaces. Our initial motivation to study such questions lies in their applications. The results obtained below enable us to complete earlier work on the structure of complemented subspaces ofLp-spaces which have extremal euclidean distance.
243 citations
TL;DR: In this article, it was shown that a bounded semialgebraic function can be reparametrized in such a way that all the derivatives up to a fixed orderk, with respect to new coordinates, are small, and the number of pieces is effectively bounded.
Abstract: We prove that a bounded semialgebraic function can be (piecewise) reparametrized in such a way that all the derivatives up to a fixed orderk, with respect to new coordinates, are small, and the number of pieces is effectively bounded.
93 citations
TL;DR: In this article, a prime ring with the centerZ and the extended centroidC is considered, and a polynomial over C in noncommuting variablesx>>\s 1, …,..., X>>\s n ∈ the ring of all 2 × 2 matrices over GF(2) is considered.
Abstract: SupposeR is a prime ring with the centerZ and the extended centroidC. Letp(x
1, …,x
n) be a polynomial overC in noncommuting variablesx
1, …,x
n. LetI be a nonzero ideal ofR andA be the additive subgroup ofRC generated by {p(a
1, …,a
n):a
1, …,a
n ∈I}. Then eitherp(x
1, …,x
n) is central valued orA contains a noncentral Lie ideal ofR except in the only one case whereR is the ring of all 2 × 2 matrices over GF(2), the integers mod 2.
83 citations
TL;DR: In this article, it was shown that the complex Grothendieck constant has an upper bound of 8/π(k petertodd 0+1) ≈ 1.40491.
Abstract: Let ϕ denote the real function
$$\varphi (k) = k\smallint _0^{\pi /2} \frac{{cos^2 t}}{{\sqrt {1 - k^2 sin ^2 t} }}dt, - 1 \leqq k \leqq 1$$
and letK
G
C
be the complex Grothendieck constant. It is proved thatK
G
C
≦8/π(k
0+1), wherek
0 is the (unique) solution to the equationϕ(k)=1/8π(k+1) in the interval [0,1]. One has 8/π(k
0+1) ≈ 1.40491. The previously known upper bound isK
G
C
≦e
1−y
≈ 1.52621 obtained by Pisier in 1976.
80 citations
TL;DR: In this paper, every ergodic transformation (X, T, ℬ,μ) has an isomorphic system (Y, U, ======Open image in new window======ν) which is uniquely ergodical and topologically mixing.
Abstract: Every ergodic transformation (X, T, ℬ,μ) has an isomorphic system (Y, U,
Open image in new window
ν) which is uniquely ergodic and topologically mixing.
59 citations
TL;DR: In this paper, the authors present an algorithm which, for a given combinatorial (d − 2)-sphereS withn vertices, determines the setC d,n(S) of rankd oriented matroids withn points and face latticeS. Since S is polytopal if and only if there is a realizable M eC c,n (S)
Abstract: The convexity theory for oriented matroids, first developed by Las Vergnas [17], provides the framework for a new computational approach to the Steinitz problem [13]. We describe an algorithm which, for a given combinatorial (d − 2)-sphereS withn vertices, determines the setC
d,n(S) of rankd oriented matroids withn points and face latticeS. SinceS is polytopal if and only if there is a realizableM eC
d,n(S), this method together with the coordinatizability test for oriented matroids in [10] yields a decision procedure for the polytopality of a large class of spheres. As main new result we prove that there exist 431 combinatorial types of neighborly 5-polytopes with 10 vertices by establishing coordinates for 98 “doubted polytopes” in the classification of Altshuler [1]. We show that for alln ≧k + 5 ≧8 there exist simplicialk-spheres withn vertices which are non-polytopal due to the simple fact that they fail to be matroid spheres. On the other hand, we show that the 3-sphereM
963
9
with 9 vertices in [2] is the smallest non-polytopal matroid sphere, and non-polytopal matroidk-spheres withn vertices exist for alln ≧k + 6 ≧ 9.
52 citations
TL;DR: In this article, it was shown that any map from a space with finitely many non-vanishing homotopy groups into a finite complex is phantom and that any fibration over a 2-connected space with finite complex and with fiber is trivial over each skeleton of the base.
Abstract: A mapf:X →Y is a phantom map if any composition off with a map from a finite complex intoX is null homotopic. The proof of the Sullivan conjecture by H. Miller enables us to understand more deeply this phenomena. We prove, among other things, that any map from a space with finitely many non-vanishing homotopy groups into a finite complex is phantom and that any fibration over a 2-connected space with finitely many non-vanishing homotopy groups and with fiber a finite complex is trivial over each skeleton of the base.
48 citations
TL;DR: In this article, it was shown that if E is a Banach lattice andS, T ∈ ℒ (E) are such that 0≦s≦T,r(s)=r(T) andr(S) is a Riesz point ofσ(T), then r(S), s, s, r(s), r(T, s) and s, t ∈ σ (E), s) are a Riez points of σ(S).
Abstract: We prove that ifE is a Banach lattice andS, T ∈ ℒ (E) are such that 0≦s≦T,r(s)=r(T) andr(T) is a Riesz point ofσ(T) thenr(S) is a Riesz point ofσ(S). We prove also some results on compact positive perturbations of positive irreducible operators and lattice homomorphisms.
43 citations
TL;DR: In this paper, it was shown that locally over a nonarchimedean field F, this correspondence is injective on generic representations (i.e. with Whittaker model) of GSp(4,F).
Abstract: Consider the θ-correspondence from GSp(4) to GSO(6). We prove that locally over a nonarchimedean fieldF, this correspondence is injective on generic representations (i.e. with Whittaker model) of GSp(4,F). We use this to show the strong multiplicity one property for irreducible, automorphic, cuspidal representations of GSp(4,A), which are generic.
42 citations
TL;DR: In this article, the existence of Poincare sequences of integers which are not van der Corput sets was proved by showing that the generic density condition for both properties are the same.
Abstract: The main purpose of this paper is to prove the existence of Poincare sequences of integers which are not van der Corput sets. This problem was considered in I. Ruzsa’s expository article [R1] (1982–83) on correlative and intersective sets. Thus the existence is shown of a positive non-continuous measureμ on the circle which Fourier transform vanishes on a set of recurrence, i.e.S={n ∈Z;\(\hat \mu \)(n)=0} is a set of recurrence but not a van der Corput set. The method is constructive and involves some combinatorial considerations. In fact, we prove that the generic density condition for both properties are the same.
TL;DR: There are exactly 37 combinatorial types of neighborly 6-polytopes with 10 vertices as discussed by the authors, and a full description is given in Section 2.2.1.
Abstract: There are exactly 37 combinatorial types of neighborly 6-polytopes with 10 vertices. A full description is given.
TL;DR: In this article, the Jacobson radical of R * U(L) for a Lie algebra over a field K which acts as K-derivations on a K-algebra R is described.
Abstract: LetL be a Lie algebra over a fieldK which acts asK-derivations on aK-algebraR. Then this action determines a crossed productR *U(L) whereU(L) is the enveloping algebra ofL. The goal of this paper is to describe the Jacobson radical ofR * U(L) forL≠0. We are most successful whenR is a p.i. algebra or Noetherian. In more general situations we at least obtain upper and lower bounds forJ(R * U(L)) which are ideals extended fromR. Furthermore, we offer an interesting example in all characteristics of a commutativeK-algebraC which admits a derivationδ such thatC isδ-prime but not semiprime.
TL;DR: In this paper, Shephard has given a criterion for the indecomposability (in the sense of Minkowski addition) of a convex polytope, in terms of strong chains of indecompositionable faces joining pairs of vertices.
Abstract: Shephard has given a criterion for the indecomposability (in the sense of Minkowski addition) of a convex polytope, in terms of strong chains of indecomposable faces joining pairs of vertices Here, this criterion is weakened, to one involving strongly connected sets of indecomposable faces meeting every facet
TL;DR: A group is an ℵ1-free abelian group iffA is a subgroup of the Boolean power Z(B) for some complete Boolean algebraB.
Abstract: A groupA is an ℵ1-free abelian group iffA is a subgroup of the Boolean power Z(B) for some complete Boolean algebraB. The Chase radicalvA=Σ{C≦A: Hom(C, Z)=0 &C is countable). The torsion class {A:vA=A} is not closed under uncountable direct products.
TL;DR: Weierstrass points are defined for invertible sheaves on integral, projective Gorenstein curves as discussed by the authors, where the set of all higher order higher order Weierstass points of a sheaf is not dense.
Abstract: Weierstrass points are defined for invertible sheaves on integral, projective Gorenstein curves. An example is given of a rational nodal curveX and an invertible sheaf ℒ of positive degree onX such that the set of all higher order Weierstrass points of ℒ is not dense inX.
TL;DR: In this article, the authors examined the weight functions that correspond to the case when the extremum for the variational principle is attained, and characterized the corresponding mappingsf *.
Abstract: Supposef*(z) is aK*-qc self-homeomorphism of the unit diskU, whereK* is the minimum possible value among all qc mappings ofU with the same boundary values asf*. It is known thatK* can be calculated by a variational principle involving mappings ofU harmonic with respect to admissible weight functions. We examine the weight functions that correspond to the case when the extremum for the variational principle is attained, and characterize the corresponding mappingsf*.
TL;DR: In this article, it was shown that any noncentral additive subgroup of R invariant under special automorphisms contains a noncentral Lie ideal under the assumption that R possesses nontrivial idempotents.
Abstract: Suppose thatR is a prime ring with the centerZ and the extended centroidC. An additive subgroupA ofR is said to be invariant under special automorphisms if (1+t)A(1+t)−1 ⊆A for allt ∈R such thatt
2=0. Assume thatR possesses nontrivial idempotents. We prove: (1) If chR ≠ 2 or ifRC ≠C
2, then any noncentral additive subgroup ofR invariant under special automorphisms contains a noncentral Lie ideal. (2) If chR=2,RC=C
2 andC ≠ {0, 1}, then the following two conditions are equivalent: (i) any noncentral additive subgroup invariant under special automorphisms contains a noncentral Lie ideal; (ii) there isα ∈Z / {0} such thatα
2
Z ⊆ {β
2:β ∈Z}.
TL;DR: In this article, the authors studied the endomorphism ring of a Σ-quasiprojective module M and gave necessary and sufficient conditions on M forS to have certain properties, such as being QF or left (F)PF.
Abstract: We study the endomorphism ringS of a Σ-quasiprojective moduleM, giving necessary and sufficient conditions onM forS to have certain properties, such as, e.g., being QF or left (F)PF.
TL;DR: In this paper, the authors studied the question of which manifold fiber over the circle in dimensions four and five is fiber-free and showed that the answer is "no" for any manifold fiber.
Abstract: This paper studies the question of which manifolds fiber over the circle in dimensions four and five.
TL;DR: In this article, a new construction of the evolution operator G(t, s) associated to a family of generators of analytic semigroups in a Banach space was proposed.
Abstract: We find a new construction of the evolution operatorG(t, s) associated to a family {A(t), 0≦t≦T} of generators of analytic semigroups in a Banach spaceX. We study the dependence ofG (t, s) ont ands, and we give regularity results for the solution of the i.v.p.u′(t)=A(t)u(t)+f(t),u(0)=x.
TL;DR: In this paper, it was shown that a suitable iteration does not collapse ℵ1 [and does not add reals] and that in such iteration, certain sealing of maximal antichains of stationary subsets of φαραβαββαρβα β is allowed.
Abstract: We prove that suitable iteration does not collapse ℵ1 [and does not add reals], ie, that in such iteration, certain sealing of maximal antichains of stationary subsets ofω
1 is allowed As an application, eg, we prove from supercompact hypotheses, mainly, the consistency of: ZFC + GCH + “for some stationary setS ⊆ω
1, {ie345-1}(ω
1)/(D
ω
1 +S) is the Levy algebra” (ie, the complete Boolean Algebra corresponding to the Levy collapse Levy (ℵ0,<ℵ2) (and we can add “a variant of PFA”) and the consistency of the same, with “Ulam property” replacing “Levy algebra”) The paper assumes no specialized knowledge (if you agree to believe in the semi-properness iteration theorem and RCS iteration)
TL;DR: In this paper, a stabilization theorem for strongly monotone and nonexpansive dynamical systems on a Banach lattice is proved and applied to a periodic-parabolic semilinear initial-boundary value problem to show the convergence of solutions towards periodic solutions.
Abstract: A stabilization theorem for discrete strongly monotone and nonexpansive dynamical systems on a Banach lattice is proved. This result is applied to a periodic-parabolic semilinear initial-boundary value problem to show the convergence of solutions towards periodic solutions.
TL;DR: In this paper, the authors give conditions ensuring the existence for an initial value (x.............. 0,v PsyNet 0) of a solution to the second-order differential inclusion problem.
Abstract: This paper gives conditions ensuring the existence for an initial value (x
0,v
0) of a solution to the second order differential inclusionx″(t) ∈F[x(t),x′(t)],x(0)=x
0,x′(0)=v
0 such thatx(t) ∈K for allt whereK is a nonempty given subset ofR
n
.
TL;DR: In this paper, the transitive orientation of a graph G with n vertices and at most n log log logn edges has been investigated and it was shown that almost every graph G,p satisfies this requirement if and only if
Abstract: Given a graphG onn vertices and a total ordering ≺ ofV(G), the transitive orientation ofG associated with ≺, denotedP(G; ≺), is the partial order onV(G) defined by settingx
TL;DR: In this article, the set of invariant measures of topologically transitive subsets of certain piecewise monotonic transformations on [0, 1] with the weak topology was studied.
Abstract: We endow the set of all invariant measures of topologically transitive subsetsL of certain piecewise monotonic transformations on [0, 1] with the weak topology. We show that the set of periodic orbit measures is dense, that the sets of ergodic, of nonatomic, and of measures with supportL are dense-sets, that the se of strongly mixing measures is of first category, and that the set of measures with zero entropy contains a denseGin/gd-set.
TL;DR: In this article, the authors studied the limit behaviour of Tkf and the Cesaro averages of this sequence, and showed that Tnf converges in distribution weakly in Lp (1
Abstract: We study the limit behaviour ofTkf and of Cesaro averagesAnf of this sequence, whenT is order preserving and nonexpansive inL1+. IfT contracts also theL∞-norm, the sequenceTnf converges in distribution, andAnf converges weakly inLp (1
TL;DR: In this article, it was shown that no triple sum of infinite sets has an affine image of it, and that no set of positive measure has affine affine images of it.
Abstract: This paper deals with the problem of existence of infinite structures in euclidean space such that every set of positive measure contains an affine image of it. We contribute to P. Erdos’ question about sequences in the real line, by showing that no triple sum of infinite sets has this property.
TL;DR: In this article, it was shown that there is no universal Eberlein compact of weight τ satisfying τ = τ and ϵ = ϵ for cardinal ϵ satisfying ϵ ≥ ϵ.
Abstract: We prove that for cardinalsτ satisfying τω=τ and forτ=ω 1, there do not exist universal Eberlein Compacts of weightτ, or universal WCG spaces of density characterτ Ifτ is a strong limit cardinal of countable cofinality such universal spaces do exist Thus under GCH universal spaces exist forτ iff cof(τ)=ω
TL;DR: In this article, it was shown that a positive linear contraction inLp (1≦p 0 independent off) implies already limnn→∞ ∞ √ Tnf −Tn+1n+ 1n + 1f √ p = 0.
Abstract: LetT be a positive linear contraction inLp (1≦p 0 independent off) implies already limnn→∞ ‖Tnf −Tn+1n+1f ‖pp=0. Several other related results as well as uniform variants of these are also given. Finally some similar results inLsu/t8 andC(X) are shown.