scholarly journals Controlled generalized fusion frame in the tensor product of Hilbert spaces

2021 ◽  
pp. 1-18
Author(s):  
Prasenjit Ghosh ◽  
Tapas Kumar Samanta
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Frame Operator ◽  
Fusion Frame ◽  
Bessel Sequences

We present controlled by operators generalized fusion frame in the tensor product of Hilbert spaces and discuss some of its properties. We also describe the frame operator for a pair of controlled $g$-fusion Bessel sequences in the tensor product of Hilbert spaces.

scholarly journals Controlled G-Frames and Their G-Multipliers in Hilbert spaces

2013 ◽  
Vol 21 (2) ◽  
pp. 223-236 ◽  
Author(s):  
Asghar Rahimi ◽  
Abolhassan Fereydooni
Keyword(s):  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Multiplier Operator ◽  
Frame Operator ◽  
Fixed Sequence ◽  
Numerical Efficiency ◽  
Bessel Sequences ◽  
Almost All

Abstract Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are opera- tors that combine (frame-like) analysis, a multiplication with a fixed sequence ( called the symbol) and synthesis. One of the last extensions of frames is weighted and controlled frames that introduced by P.Balazs, J-P. Antoine and A. Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Also g-frames are the most popular generalization of frames that include almost all of the frame extensions. In this manuscript the concept of the controlled g- frames will be defined and we will show that controlled g-frames are equivalent to g-frames and so the controlled operators C and C' can be used as preconditions in applications. Also the multiplier operator for this family of operators will be introduced and some of its properties will be shown.

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 A New Inequality for Frames in Hilbert Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Zhong-Qi Xiang
Keyword(s):  
Linear Operator ◽  
Hilbert Spaces ◽  
Bounded Linear Operator ◽  
Bounded Linear ◽  
Bessel Sequences

We obtain a new inequality for frames in Hilbert spaces associated with a scalar and a bounded linear operator induced by two Bessel sequences. It turns out that the corresponding results due to Balan et al. and Găvruţa can be deduced from our result.

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.

Construction of g-fusion frames in Hilbert spaces

2020 ◽  
Vol 23 (02) ◽  
pp. 2050015
Author(s):  
Vahid Sadri ◽  
Gholamreza Rahimlou ◽  
Reza Ahmadi ◽  
Ramazan Zarghami Farfar
Keyword(s):  
Hilbert Spaces ◽  
Closed Range ◽  
Fusion Frames ◽  
Interesting Topic ◽  
Fusion Frame

After introducing g-frames and fusion frames by Sun and Casazza, respectively, combining these frames together is an interesting topic for research. In this paper, we introduce the generalized fusion frames or g-fusion frames for Hilbert spaces and give characterizations of these frames from the viewpoint of closed range and g-fusion frame sequences. Also, the canonical dual g-fusion frames are presented and we introduce a Parseval g-fusion frame.

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 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.

Sign in / Sign up

Export Citation Format

Share Document