An operator theory approach to the approximate duality of Hilbert space frames

2020 ◽  
Vol 489 (2) ◽  
pp. 124177
Author(s):  
Morteza Mirzaee Azandaryani
Keyword(s):  
Hilbert Space ◽  
Operator Theory ◽  
Theory Approach ◽  
Space Frames ◽  
Approximate Duality

Abstract Plancherel (Trace) Formulas over Homogeneous Spaces of Compact Groups

2017 ◽  
Vol 60 (1) ◽  
pp. 111-121 ◽  
Author(s):  
Arash Ghaani Farashahi
Keyword(s):  
Hilbert Space ◽  
Operator Theory ◽  
Closed Subgroup ◽  
Homogeneous Spaces ◽  
Compact Groups ◽  
Theory Approach ◽  
Coset Space ◽  
Trace Formulas ◽  
Left Coset ◽  
Abstract Notion

AbstractThis paper introduces a unified operator theory approach to the abstract Plancherel (trace) formulas over homogeneous spaces of compact groups. LetGbe a compact group and letHbe a closed subgroup ofG. LetG/Hbe the left coset space ofHinGand letμbe the normalized G-invariant measure onG-Hassociated with Weil’s formula. Then we present a generalized abstract notion of Plancherel (trace) formula for the Hilbert spaceL2(G/H,μ).

scholarly journals States which have a trace-like property relative to a C*-subalgebra of B(H)

1976 ◽  
Vol 17 (2) ◽  
pp. 158-160
Author(s):  
Guyan Robertson
Keyword(s):  
Hilbert Space ◽  
Spectral Radius ◽  
Operator Theory ◽  
Linear Operators ◽  
Operator Norm ◽  
Identity Operator ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Image Position

In what follows, B(H) will denote the C*-algebra of all bounded linear operators on a Hilbert space H. Suppose we are given a C*-subalgebra A of B(H), which we shall suppose contains the identity operator 1. We are concerned with the existence of states f of B(H) which satisfy the following trace-like relation relative to A:Our first result shows the existence of states f satisfying (*), when A is the C*-algebra C*(x) generated by a normaloid operator × and the identity. This allows us to give simple proofs of some well-known results in operator theory. Recall that an operator × is normaloid if its operator norm equals its spectral radius.

M-Matrices and Generalizations Using an Operator Theory Approach

SIAM Review ◽  
1978 ◽  
Vol 20 (2) ◽  
pp. 213-244 ◽  
Author(s):  
Johann Schröder
Keyword(s):  
Operator Theory ◽  
Theory Approach

scholarly journals Sums of Hilbert space frames

2009 ◽  
Vol 351 (2) ◽  
pp. 579-585 ◽  
Author(s):  
Sofian Obeidat ◽  
Salti Samarah ◽  
Peter G. Casazza ◽  
Janet C. Tremain
Keyword(s):  
Hilbert Space ◽  
Space Frames

A note on the stability of g-frames in Hilbert C*-modules

2016 ◽  
Vol 14 (04) ◽  
pp. 1650031 ◽  
Author(s):  
Zhong-Qi Xiang
Keyword(s):  
Hilbert Space ◽  
Lower Bound ◽  
Stability Result ◽  
Complete Proof ◽  
Perturbation Theorem ◽  
Equivalent Definition ◽  
General Perturbation ◽  
Space Frames ◽  
The Stability ◽  
Definition Of

Recently, Rashidi-Kouchi et al. devoted their efforts to giving analogs of the Casazza–Christensen general perturbation theorem of Hilbert space frames for the case of g-frames in Hilbert C*-modules. We found, however, that in the proof they did not obtain the lower bound inequality of g-frames in Hilbert C*-modules. In this paper, we establish an equivalent definition of g-frames in Hilbert C*-modules, using it we present a complete proof for the stability result given by them.

scholarly journals Spectrums of Solvable Pantograph Differential-Operators for First Order

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Z. I. Ismailov ◽  
P. Ipek
Keyword(s):  
Hilbert Space ◽  
Differential Operator ◽  
Operator Theory ◽  
Differential Operators ◽  
Finite Interval ◽  
Exact Formula ◽  
Operator Expression ◽  
Minimal Operator ◽  
First Order ◽  
Delay Differential

By using the methods of operator theory, all solvable extensions of minimal operator generated by first order pantograph-type delay differential-operator expression in the Hilbert space of vector-functions on finite interval have been considered. As a result, the exact formula for the spectrums of these extensions is presented. Applications of obtained results to the concrete models are illustrated.

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