Showing papers in "Journal of Functional Analysis in 1991"

TL;DR: The concept of real rank of a C ∗ -algebra is introduced as a non-commutative analogue of dimension in this paper, and it is shown that real rank zero is equivalent to the previously defined conditions FS and HP, and is invariant under strong Morita equivalence, in particular under stable isomorphism.

TL;DR: In this paper, a Hermitian operator A with gaps (αj, βj) (1 ⩽ j⩽ m ⩾ ∞) is studied and the self-adjoint extensions which put exactly kj < ∞ eigenvalues into each gap are described in terms of boundary conditions.

TL;DR: In this paper, the authors studied a class of Banach space operators patterned after the weighted backward shifts on Hilbert space, and showed that any non-scalar operator in the commutant of one of these generalized backward shifts has a dense, invariant linear manifold whose non-zero members are cyclic vectors.

TL;DR: In this article, an abstract perturbation theorem is applied to derive global in time Lq estimates for the Cauchy problem and Lq − Ls estimates for nonstationary Stokes equations in exterior domains.

TL;DR: In this article, the authors studied the long-time behavior of small solutions of the initial value problem for the generalized Korteweg-de Vries equation and showed that the solution tends to zero in the supremum norm.

TL;DR: In this article, it was shown that if p, q ϵ A are projections and τ(p) < τ(q) for all quasitraces τ on A, then p ≲ q (in the sense of Murray and von Neumann).

TL;DR: In this article, the authors studied the critical points at infinity of the variational problem, in which the failure of the Palais-Smale condition is the main obstacle for solving equations of type (4).

TL;DR: In this article, the authors lay the foundations for a systematic study of tensor products of subspaces of C∗-algebras and employ various notions of duality.

TL;DR: In this paper, the classical Sobolev inequality ∥▽ϑ∥ 2 2 − S ∥ϑ ∥ 2 ∗ 2 ⩾αd(ϑ, M) 2, ∥∽∥2 2 −s 2 √ √ n 2, 2 n ∗ = 2n (n − 2) and n > 2.

TL;DR: In this article, a theorem characterizing Gaussian functions and a strict superaddivity property of the Fisher information were proved for R n equipped with Lebesgue measure and with Gauss measure.

TL;DR: In this paper, the space (S ∗ of Hida distributions is characterized in terms of analytic properties of the Fourier transformation of its elements, and the space is characterized by the Fouriers transformation of the elements.

TL;DR: In this article, it was shown that the large time behavior of solutions of the convection-diffusion equation u t − Δu = a · ▽(¦u¦ q − 1 u) in (0, ∞) × R N with a ϵ R N and q ⩾ 1 + 1 N, N ⩽ 1.

TL;DR: In this article, it was shown that if an operator T ∗ does not have any eigenvalue and that the union of the spectrum of T and the unit circle is a connected set, then it is hypercyclic.

TL;DR: In this paper, the authors obtained a representation theorem for module maps defined on the algebra K(H) of compact operators, which is used to show that the Haagerup tensor product of two operator algebras enjoys strong versions of Tomita's commutant theorem and the slice map property.

TL;DR: In this article, the Peter-Weyl theorem for SUq(2) and the matrix elements of these unitary representations are explicitly expressed in terms of little q-Jacobi polynomials which are known as q-analogues of orthogonal polynomial.

TL;DR: In this paper, the authors studied the spectral decomposition of the Heisenberg Laplacian operator in the free step of harmonic analysis and showed that it is bounded from Lp to Lq if and only if p = (2n + 2)(2n+ 1) and q = 2n+ 2.

TL;DR: In this paper, the essential spectrum of the Neumann Laplacian on singular domains of the type "rooms and passages" or "combs" is determined from geometric data.

TL;DR: In this article, it was shown that the heat kernels for H 0 and H 0 decay at the same rate at the boundary of the Kato class. But the results were not applicable to smooth domains.

TL;DR: In this paper, a coupling method was used to give gradient estimates for solutions to (12 Δ + Z)u = 0 on a manifold, where the size of the gradient depends on a lower bound on the Ricci curvature of the manifold and bounds on the vector field Z.

TL;DR: For non-trivial α, β these bicrossproduct Hopf-von Neumann algebras are non-commutative and non-cocommutative as discussed by the authors.

TL;DR: In this paper, it was shown that for every Borel vector field f, there exists a function u of class C 1 whose gradient Du agrees with f outside a set of arbitrary small measure.

TL;DR: In this article, two invariants of pairs of almost commuting unitary matrices have been defined and used to identify those pairs which are bounded away from commuting pairs, denoted k(U, V) for unitaries U,VϵMn( C ).

TL;DR: In this article, a logarithmic Sobolev inequality was deduced for all 0 < p ⩽ q < t8 where the Lp norms are taken with respect to the measure dμh above.

TL;DR: In this article, the gradient estimates and Harnack inequalities for positive solutions of nonlinear parabolic and nonlinear elliptic equations (Δ − ∂ ∂t ) u(x, t) + h(x and t)u α (x,t) = 0 and Δu + b · ▽u + hu α = 0 on Riemannian manifolds were derived.

TL;DR: In this paper, the Efimov effect of three-body Schrodinger operators was studied under the assumption that pair potentials fall off with order O(¦x¦ −ϱ ), ϱ > 2, at infinity and that all three two-body subsystems have a zero resonance energy.

TL;DR: In this article, the authors investigated the large-time behavior of solutions to the nonlinear heat-conduction equation with absorption, and they proved that u converges as t → ∞ to a unique self-similar function which is a contracted version of one of the asymptotic profiles of the nonabsorptive problem, the same for any initial data.

TL;DR: In this paper, it was shown that the free product of the unital positive defined functions of a family of B-bimodule maps Qi: A, + C is completely positive on the "biggest" amalgamated free product i.A i.

TL;DR: In this article, a logarithmic Sobolev inequality for the Lie algebra valued Brownian motion is derived by a method of inheritance from the known inequalities for the value of the Brownian bridge measure on the loop group.

TL;DR: In this paper, it was shown that the Haagerup tensor product V ⊗h W for operator spaces V and W preserves complete quotient maps and is self-dual.

TL;DR: In this article, Chandra, Helgason, Trombi and Varadarajan give a short proof of their results, based on the Paley-Wiener theorem.