Frame representations via suborbits of bounded operators

2019 ◽  
Author(s):  
Ole Christensen ◽  
Marzieh Hasannasab
Keyword(s):  
Bounded Operators ◽  
Frame Representations

scholarly journals Dynamical sampling and frame representations with bounded operators

2018 ◽  
Vol 463 (2) ◽  
pp. 634-644 ◽  
Author(s):  
Ole Christensen ◽  
Marzieh Hasannasab ◽  
Ehsan Rashidi
Keyword(s):  
Bounded Operators ◽  
Frame Representations

scholarly journals G-frame representations with bounded operators

2020 ◽  
pp. 2050078
Author(s):  
Yavar Khedmati ◽  
Fatemeh Ghobadzadeh
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Bounded Operators ◽  
Index Set ◽  
Translation Invariant ◽  
Fusion Frames ◽  
Generalized Translation ◽  
Special Cases ◽  
Frame Representations

Dynamical sampling, as introduced by Aldroubi et al., deals with frame properties of sequences of the form [Formula: see text], where [Formula: see text] belongs to Hilbert space [Formula: see text] and [Formula: see text] belongs to certain classes of bounded operators. Christensen et al. studied frames for [Formula: see text] with index set [Formula: see text] (or [Formula: see text]), that has representations in the form [Formula: see text] (or [Formula: see text]). As frames of subspaces, fusion frames and generalized translation invariant systems are the special cases of [Formula: see text]-frames, the purpose of this paper is to study and get sufficient conditions for [Formula: see text]-frames [Formula: see text] (or [Formula: see text] having the form [Formula: see text] [Formula: see text] (or [Formula: see text] [Formula: see text]). Also, we get the relation between representations of dual [Formula: see text]-frames with index set [Formula: see text]. Finally, we study stability of [Formula: see text]-frame representations under some perturbations.

scholarly journals The dual of the space of bounded operators on a Banach space

2021 ◽  
Vol 8 (1) ◽  
pp. 48-59
Author(s):  
Fernanda Botelho ◽  
Richard J. Fleming
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Dual Space ◽  
Tensor Products ◽  
Bounded Operators ◽  
Projective Tensor Product ◽  
Projective Tensor

Abstract Given Banach spaces X and Y, we ask about the dual space of the 𝒧(X, Y). This paper surveys results on tensor products of Banach spaces with the main objective of describing the dual of spaces of bounded operators. In several cases and under a variety of assumptions on X and Y, the answer can best be given as the projective tensor product of X ** and Y *.

scholarly journals The spectral theorem for well-bounded operators

1993 ◽  
Vol 54 (3) ◽  
pp. 334-351 ◽  
Author(s):  
Ian Doust ◽  
Qiu Bozhou
Keyword(s):  
Functional Calculus ◽  
Continuous Functions ◽  
Weak Compactness ◽  
Compact Interval ◽  
Spectral Theorem ◽  
Type B ◽  
Bounded Operators ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous

AbstractWell-bounded operators are those which possess a bounded functional calculus for the absolutely continuous functions on some compact interval. Depending on the weak compactness of this functional calculus, one obtains one of two types of spectral theorem for these operators. A method is given which enables one to obtain both spectral theorems by simply changing the topology used. Even for the case of well-bounded operators of type (B), the proof given is more elementary than that previously in the literature.

scholarly journals TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY

2010 ◽  
Vol 88 (2) ◽  
pp. 205-230 ◽  
Author(s):  
CHRISTOPH KRIEGLER ◽  
CHRISTIAN LE MERDY
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Unconditional Basis ◽  
Compact Set ◽  
Bounded Operators ◽  
Space Setting ◽  
Uniformly Bounded

AbstractLet K be any compact set. The C*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these results to the Banach space setting, using the key concept ofR-boundedness. Then we apply these results to operators with a uniformly bounded H∞-calculus, as well as to unconditionality on Lp. We show that any unconditional basis on Lp ‘is’ an unconditional basis on L2 after an appropriate change of density.

Infinitely entangled states

2003 ◽  
Vol 3 (4) ◽  
pp. 281-306
Author(s):  
M. Keyl ◽  
D. Schlingemann ◽  
R.F. Werner
Keyword(s):  
Hilbert Spaces ◽  
Degrees Of Freedom ◽  
Entangled States ◽  
Entangled State ◽  
Bounded Operators ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Density Operators ◽  
Fundamental Paper ◽  
Extended Notion

For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as a resource for tasks like the teleportation of arbitrarily many qubits. We show that appropriate states cannot be obtained by density operators in an infinite dimensional Hilbert space. However, using techniques for the description of infinitely many degrees of freedom from field theory and statistical mechanics, such states can nevertheless be constructed rigorously. We explore two related possibilities, namely an extended notion of algebras of observables, and the use of singular states on the algebra of bounded operators. As applications we construct the essentially unique infinite analogue of maximally entangled states, and the singular state used heuristically in the fundamental paper of Einstein, Rosen and Podolsky.

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