scholarly journals Stability and Boundedness of Solutions to Nonautonomous Parabolic Integrodifferential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Michael Gil'
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Integrodifferential Equations ◽  
Stability Of Solutions ◽  
Boundedness Of Solutions ◽  
Norm Estimates ◽  
Operator Functions

We consider a class of linear nonautonomous parabolic integrodifferential equations. We will assume that the coefficients are slowly varying in time. Conditions for the boundedness and stability of solutions to the considered equations are suggested. Our results are based on a combined usage of the recent norm estimates for operator functions and theory of equations on the tensor product of Hilbert spaces.

Extension of normal functionals on W*-tensor products

1975 ◽  
Vol 78 (2) ◽  
pp. 301-307 ◽  
Author(s):  
Simon Wassermann
Keyword(s):  
Representation Theory ◽  
Tensor Product ◽  
Hilbert Spaces ◽  
General Result ◽  
Von Neumann Algebras ◽  
Tensor Products ◽  
Von Neumann ◽  
Hilbert Algebras ◽  
Special Cases

A deep result in the theory of W*-tensor products, the Commutation theorem, states that if M and N are W*-algebras faithfully represented as von Neumann algebras on the Hilbert spaces H and K, respectively, then the commutant in L(H ⊗ K) of the W*-tensor product of M and N coincides with the W*-tensor product of M′ and N′. Although special cases of this theorem were established successively by Misonou (2) and Sakai (3), the validity of the general result remained conjectural until the advent of the Tomita-Takesaki theory of Modular Hilbert algebras (6). As formulated, the Commutation theorem is a spatial result; that is, the W*-algebras in its statement are taken to act on specific Hilbert spaces. Not surprisingly, therefore, known proofs rely heavily on techniques of representation theory.

scholarly journals A COMPLETELY ENTANGLED SUBSPACE OF MAXIMAL DIMENSION

2006 ◽  
Vol 04 (02) ◽  
pp. 325-330 ◽  
Author(s):  
B. V. RAJARAMA BHAT
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Product Formula ◽  
Maximal Dimension ◽  
Maximum Dimension ◽  
Dimension Formula ◽  
Finite Dimensional ◽  
Minimum Dimension ◽  
Orthogonal Product ◽  
Product Vector

Consider a tensor product [Formula: see text] of finite-dimensional Hilbert spaces with dimension [Formula: see text], 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of [Formula: see text] with no non-zero product vector is known to be d1 d2…dk - (d1 + d2 + … + dk + k - 1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and show that it has the minimum dimension possible for an unextendible product basis of not necessarily orthogonal product vectors.

scholarly journals Rothe's method to semilinear hyperbolic integrodifferential equations

1990 ◽  
Vol 3 (4) ◽  
pp. 245-252 ◽  
Author(s):  
D. Bahaguna ◽  
A. K. Pani ◽  
V. Raghavendra
Keyword(s):  
Strong Solution ◽  
Hilbert Spaces ◽  
Integrodifferential Equations ◽  
Unique Strong Solution ◽  
Rothe's Method ◽  
Rothe’S Method

In this paper we consider an application of Rothe's method to abstract semi-linear hyperbolic integrodifferential equations in Hilbert spaces. With the aid of Rothe's method we establish the existence of a unique strong solution.

FUSION FRAMES AND g-FRAMES IN HILBERT C*-MODULES

2008 ◽  
Vol 06 (03) ◽  
pp. 433-446 ◽  
Author(s):  
AMIR KHOSRAVI ◽  
BEHROOZ KHOSRAVI
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Hilbert Spaces ◽  
Frame Theory ◽  
Fusion Frames ◽  
Perturbation Result ◽  
Fusion Frame

The notion of frame has some generalizations such as frames of subspaces, fusion frames and g-frames. In this paper, we introduce fusion frames and g-frames in Hilbert C*-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. We also generalize a perturbation result in frame theory to g-frames in Hilbert spaces. We also show that tensor product of fusion frames (g-frames) is a fusion frame (g-frame) and tensor product of resolution of identity is a resolution of identity.

scholarly journals Multiplicities in the Tensor Product of Finite-Dimensional Representations of Discrete Groups

1978 ◽  
Vol 21 (1) ◽  
pp. 17-19
Author(s):  
Dragomir Ž. Djoković
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Unitary Representations ◽  
Vector Spaces ◽  
Closed Field ◽  
Discrete Groups ◽  
Algebraically Closed Field ◽  
Finite Dimensional ◽  
Irreducible Unitary Representations

Let G be a group and ρ and σ two irreducible unitary representations of G in complex Hilbert spaces and assume that dimp ρ= n < ∞. D. Poguntke [2] proved that is a sum of at most n2 irreducible subrepresentations. The case when dim a is also finite he attributed to R. Howe.We shall prove analogous results for arbitrary finite-dimensional representations, not necessarily unitary. Thus let F be an algebraically closed field of characteristic 0. We shall use the language of modules and we postulate that allour modules are finite-dimensional as F-vector spaces. The field F itself will be considered as a trivial G-module.

scholarly journals Quantum mereology in finite quantum mechanics

2021 ◽  
Vol 29 (4) ◽  
pp. 347-360
Author(s):  
Vladimir V. Kornyak
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Tensor Product ◽  
Quantum System ◽  
Hilbert Spaces ◽  
Model Based

Any Hilbert space with composite dimension can be factored into a tensor product of smaller Hilbert spaces. This allows us to decompose a quantum system into subsystems. We propose a model based on finite quantum mechanics for a constructive study of such decompositions.

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