Banach spaces related to integrable group representations and their atomic decompositions. Part II

1989 ◽  
Vol 108 (2-3) ◽  
pp. 129-148 ◽  
Author(s):  
Hans G. Feichtinger ◽  
K. H. Gr�chenig
Keyword(s):  
Banach Spaces ◽  
Group Representations ◽  
Atomic Decompositions

scholarly journals Approximative K-atomic decompositions and frames in Banach spaces

2018 ◽  
Vol 26 (1/2) ◽  
pp. 153-166
Author(s):  
Shah Jahan
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Atomic Decomposition ◽  
Necessary Conditions ◽  
Bounded Operator ◽  
Special Kind ◽  
Frame Theory ◽  
Bessel Sequence ◽  
Atomic Decompositions ◽  
Counter Example

L. Gǎvruţa (2012) introduced a special kind of frames, named K-frames, where K is an operator, in Hilbert spaces, which is significant in frame theory and has many applications. In this paper, first of all, we have introduced the notion of approximative K-atomic decomposition in Banach spaces. We gave two characterizations regarding the existence of approximative K-atomic decompositions in Banach spaces. Also some results on the existence of approximative K-atomic decompositions are obtained. We discuss several methods to construct approximative K-atomic decomposition for Banach Spaces. Further, approximative d-frame and approximative d-Bessel sequence are introduced and studied. Two necessary conditions are given under which an approximative d-Bessel sequence and approximative d-frame give rise to a bounded operator with respect to which there is an approximative K-atomic decomposition. Example and counter example are provided to support our concept. Finally, a possible application is given.

scholarly journals Disintegration of Group Representations on Direct Integrals of Banach Spaces

2019 ◽  
Vol 09 (11) ◽  
pp. 879-924
Author(s):  
Simon Joseph ◽  
Fatin Saeed ◽  
Nagat Suoliman ◽  
Mohammed Khanfoor ◽  
Abd Elmotaleb Abd Ellah
Keyword(s):  
Banach Spaces ◽  
Group Representations

scholarly journals Construction of generalized atomic decompositions in Banach spaces

2014 ◽  
Vol 2 (3) ◽  
Author(s):  
Raj Kumar ◽  
Mahesh Joshi ◽  
Ram Singh ◽  
Ashok Sah
Keyword(s):  
Banach Spaces ◽  
Atomic Decompositions

scholarly journals Group representations in non-archimedean Banach spaces

1974 ◽  
Vol 1 ◽  
pp. 329-340 ◽  
Author(s):  
A. C. M. van Rooij ◽  
W. H. Schikhof
Keyword(s):  
Banach Spaces ◽  
Group Representations

SIP Xd-frames and their perturbations in uniformly convex Banach spaces

2014 ◽  
Vol 12 (03) ◽  
pp. 1450024
Author(s):  
Xianwei Zheng ◽  
Shouzhi Yang
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Separable Banach Space ◽  
Inner Product ◽  
Uniformly Convex ◽  
Atomic Decompositions ◽  
Banach Frames ◽  
Uniformly Convex Banach Spaces ◽  
Bk Space ◽  
The Relationship

In this paper, we introduce the definitions of SIP-I and SIP-II Xd-frames in a uniformly convex, separable Banach space X with respect to a BK-space Xd (here SIP represents semi-inner product), both of them are defined as sequence of elements in X. We characterize SIP-I and SIP-II Xd-frames in terms of the corresponding synthesis and analysis operators, respectively, then we consider perturbations for both of them. Furthermore, we also introduce the definitions of SIP Banach frames and SIP atomic decompositions. Under certain assumptions, we establish the relationship between SIP Banach frames and SIP atomic decompositions, and therefore obtain reconstruction formulas for every element in X and X* by using a pair of SIP-I and SIP-II Xd-frames for X. Finally, we discuss perturbations of SIP Banach frames and SIP atomic decompositions.

scholarly journals On the cohomology of weakly almost periodic group representations

2014 ◽  
Vol 06 (02) ◽  
pp. 153-165 ◽  
Author(s):  
Uri Bader ◽  
Christian Rosendal ◽  
Roman Sauer
Keyword(s):  
Banach Spaces ◽  
Periodic Group ◽  
Decomposition Theorem ◽  
Group Cohomology ◽  
Continuous Group ◽  
Restriction Map ◽  
Almost Periodic ◽  
Group Representations ◽  
Reflexive Banach Spaces ◽  
Weakly Almost Periodic

We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll–Nardzewski fixed point theorem, we prove a vanishing result for the restriction map (with respect to a subgroup) in the reduced cohomology of weakly periodic representations. Combined with the Alaoglu–Birkhoff decomposition theorem, this generalizes and complements theorems on continuous group cohomology by several authors.

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