Showing papers on "Multiplication operator published in 1991"
TL;DR: In this article, it was shown that the space of completely bounded maps between two operator spaces can be realized as an operator space, and that with appropriate matricial norms the dual of the operator space V is completely isometric to a linear space of operators.
Abstract: The authors previously observed that the space of completely bounded maps between two operator spaces can be realized as an operator space In particular, with the appropriate matricial norms the dual of an operator space V is completely isometric to a linear space of operators This approach to duality enables one to formulate new analogues of Banach space concepts and results In particular, there is an operator space version ⊗μ of the Banach space projective tensor product , which satisfies the expected functorial properties As is the case for Banach spaces, given an operator space V, the functor W |—> V ⊗μ W preserves inclusions if and only if is an injective operator space
155 citations
TL;DR: In this paper, a relative number state (RNS) representation of a system composed of two distinguishable subsystems is proposed, and a phase variable as a quantum mechanical operator conjugate to the relative number operator is defined based on the RNS representation space.
Abstract: A relative number state (RNS) representation of a system composed of two distinguishable subsystems is proposed. A phase variable as a quantum mechanical operator conjugate to a relative number operator is defined based on the RNS representation space. The phase operator is expressed as a unitary exponential operator. The properties of the relative number operator, the phase operator, and their eigenstates are investigated in detail. The phase variable has a maximum uncertainty in any stationary state. Also, a time operator as a dynamical variable can be defined in the RNS representation space. The RNS representation is closely related to the Liouville space formulation and to thermofield dynamics. The RNS representation is shown to be a suitable method for investigating the Josephson junction with ultrasmall capacitance. A basic formulation of number‐phase quantization in the Josephson junction is given in terms of the RNS representation.
46 citations
TL;DR: In this article, a control system is described by a diagonal semigroup on the state space and by an unbounded control operator B defined on the input space l 2, and a condition called the operator Carleson measure criterion is formulated.
43 citations
38 citations
TL;DR: In this article, a method for obtaining the failure frequency of any system whose structure function is coherent is introduced, which can be expressed as a unique differential operator, regardless of the form of expression, and can be obtained by applying the differential operator to the availability expression.
Abstract: A method for obtaining the failure frequency of any system whose structure function is coherent is introduced. The relationship of the availability to the failure frequency can be expressed as a unique differential operator. In this way, regardless of the form of expression, the failure frequency can be obtained by applying the differential operator to the availability expression. Some reduction techniques are shown to be useful in evaluating failure frequency by means of this differential operator. If the reduction formulas are approximate rather than exact, it is generally difficult to apply the operator. This operator is tested on a special type of approximate reduction (the quadrilateral-star transformation). A numerical example for this reduction is presented. >
16 citations
TL;DR: In this paper, the authors characterise multiplication operators on locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm.
Abstract: If V is a system of weights on a completely regular Hausdorff space X and E is alocally convex space, then CV 0 ( X, E ) and CV b ( X, E ) are locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm. In this paper we characterise multiplication operators on these spaces induced by scalar-valued and vector-valued mappings. Many examples are presented to illustrate the theory.
12 citations
11 citations
TL;DR: In this paper, a characterization of almost periodic strongly continuous Sine operator function is given, and in a Hilbert space, it is shown that the almost periodicity of a Sine function implies that of the corresponding Cosine function.
Abstract: In this paper, a characterization of almost periodic strongly continuous Sine operator function is given, and in a Hilbert space, it is shown that the almost periodicity of a Sine operator function implies that of the corresponding Cosine operator function.
11 citations
TL;DR: In this article, it was shown that weighted composition operators whose weights are multiplicative coboundaries are isometrically isomorphic to the composition operator induced by the same transformation on the same space with an equivalent measure.
10 citations
Journal Article•
TL;DR: In this article, the authors prove that the composition operator F maps the space AC[a,b] into itself if and only if f satisfies a local Lipschitz condition on R.
Abstract: Denote by F the composition operator generated by a given function f: R --> R, acting on the space of absolutely continuous functions. In this paper we prove that the composition operator F maps the space AC[a,b] into itself if and only if f satisfies a local Lipschitz condition on R.
Journal Article•
TL;DR: In this paper, the conditions générales d'utilisation (http://www.compositio.org/conditions) of the agreement with the Foundation Compositio Mathematica are defined.
Abstract: © Foundation Compositio Mathematica, 1991, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
31 May 1991
TL;DR: The defining power of finite recursive specifications over the theory with + and · and λ (the state operator) over a finite set of states is found to be greater than that of the same theory without state operator.
Abstract: We investigate the defining power of finite recursive specifications over the theory with + (alternative composition) and · (sequential composition) and λ (the state operator) over a finite set of states, and find that it is greater than that of the same theory without state operator. Thus, adding the state operator is an essential extension of BPA (the theory of processes over +, ·). On the other hand, applying the state operator to a regular process again gives a regular process. As a limiting result in the other direction, we find that not all PA-processes (where also parallel composition λ is present) can be defined over BPA plus state operator.
TL;DR: In this article, a necessary and sufficient condition for existence of linear eigencurves is given for the existence of σλ + o(λ) = σ ε + β + o (1) for the eigenvalues of λS − T as λ→ ± ∞.
Abstract: Let T be a selfadjoint uniformly elliptic partial differential operator on a bounded domain in Rn, and let S be a (possibly indefinite) L∞ multiplication operator. Estimates of the form σλ + o(λ) and σλ + β + o(1) are sought for the eigenvalues μ(λ) of λS – T as λ→ ±∞. A necessary and sufficient condition is also obtained for existence of linear eigencurves, i.e. μ(λ) = σλ + β.
TL;DR: In this paper, the authors consider the problem of approximate determination of isolated bounded-norm solutions of nonlinear operator equations in a Hilbert space and construct closed balls such that the existence and uniqueness conditions are satisfied in each ball.
Abstract: We consider the problem of approximate determination of isolated bounded-norm solutions of nonlinear operator equations in a Hilbert space. Closed balls are constructed, such that the existence and uniqueness conditions are satisfied in each ball.
Posted Content•
TL;DR: The puncture operator in c=1 Liouville gravity is identified as the discrete state with spin J=1/2 and the recursion relation involving this operator is derived by the operator product expansion.
Abstract: We identify the puncture operator in c=1 Liouville gravity as the discrete state with spin J=1/2. The correlation functions involving this operator satisfy the recursion relation which is characteristic in topological gravity. We derive the recursion relation involving the puncture operator by the operator product expansion. Multiple point correlation functions are determined recursively from fewer point functions by this recursion relation.
TL;DR: In this article, a space of functions contained in the Bergman space, but not necessarily in U, is described and a subspace consisting of functions which induce compact multiplication operators is identified.
Abstract: We describe a space of functions contained inxxLx℞(D)⋂C(D ⋃G) but not necessarily inU. We give a representation of these functions as bounded multiplication operators on the Bergman spacexxLxa2 and identify the subspace consisting of functions which induce compact multiplication operators. We also describe a newC*-subalgebra ofxxLx℞(D) which we conjecture to be a proper super-set ofU.
TL;DR: In this article, Alexiewicz and Orlicz showed that a light variant of the implication remains valid in case of weak domains of operator valued matrices, where the set of all elements of a matrix is weakly sectionally convergent.
Abstract: holds for every separable FK-space F, for every FK-space E containing the set (p of all finite (real er complex valued) sequences, and for each sequence space M having suitable factor sequences; thereby W e denotes the set of all elements of E being weakly sectionally convergent. This result was proved by the first au thor [4] under the addit ional assumption tha t M is an FK-AB-space and by bo th authors [5] under the same assumption and in the special case tha t is a summabil i ty domain. For the "his tory" of such theorems of Mazur-Orl icz type we refer for example t o [6]. On the base of t he examinat ions of distinguished subspaces of FK-spaces over an F-space X (FK(X)spaces) in [7] (see also [2] and [10]) we prove in section 2 of the present paper t h a t the implication ( * ) remains t rue if, in addition, E is an FK(X)-space eind F is a summabil i ty domain of a suitable operator valued matr ix . Proving an inclusion theorem we show in section 3 tha t a light variant of implication ( » ) remains t rue in case of weak domains of operator valued matrices. In section 4 we get quite similar to the classical case as immediate corollaries of the Theorems of Mazur-Orl icztype some consistency theorems containing, for example, operator bounded consistency theorems due to A. Alexiewicz and W. Orlicz (see [1] and [9, Theorem 6.27]). We complete the paper with an example of operator valued matrices related to almost convergence which proves tha t it is of mathemat ica l interest to consider weak domains of opera tor valued matrices.
01 Jan 1991
TL;DR: $C^*$-algebras associated to two-step nilpotent groups by L. Baggett and J. Smith Representation of symplectic vector spaces obtained as unitary dilations by P. Jorgensen and D. R. Pitts.
TL;DR: In this article, the question of when two composition operators are equivalent in some sense is studied, and it turns out that the only equivalences are those that are induced by an invertible composition operator.
Abstract: If ϕ is an analytic function taking the unit disk into itself then the composition operatorCϕ can be defined on the Hardy spaceHp(D) byCϕ(f)=foϕ. In this work, the question of when two of these operators are equivalent in some sense is studied. In some cases, it turns out that the only equivalences are those that are induced by an invertible composition operator. However, other cases are exhibited in which there are equivalences that are not induced by an invertible composition operator.
TL;DR: In this paper, the authors give a simple proof of the known fact that such operators can be reduced to an upper triangular form via a unitary conjugation, which is a generalization of a result of J. Phillips who solved this approximation problem for the operator bound norm.
TL;DR: In this paper, the wave function is considered as the kernel of a many-particle operator, and the corresponding operator equation automatically leads to a convenient matrix algorithm for full configuration interaction calculations.
Abstract: We discuss modern trends in the theory and practice of full configuration interaction calculations. We pay the most attention to the wave operator method, in which the wave function is considered as the kernel of a many-particle operator. The corresponding operator equation, equivalent to the Schrodinger equation, automatically leads to a convenient matrix algorithm. We also discuss an alternative approach based on the pairing operator, generalizing the construction of the wave function in the method of one-particle spin-pairing amplitudes.
TL;DR: In this article, a linear continuous right inverse operator of a convolution operator in spaces of analytic functions with an exponential basis is given, which is similar to the one described in this paper.
Abstract: We give a description of a linear continuous right inverse operator of a convolution operator in spaces of analytic functions with an exponential basis.
TL;DR: In this paper, the concept of quasinormal and subnormal operators on a Krein space was introduced, and it was shown that every quasiannormal operator is subnormal.
Abstract: In this paper we introduce the concept of quasinormal and subnormal operators on a Krein space and prove that every quasinormal operator is subnormal. And some conditions for an operator on a Hilbert space to be a subnormal operator in the Krein space sense are obtained.