RETRO K-BANACH FRAMES IN BANACH SPACES

CHANDER SHEKHAR; TARA .; GHANSHYAM SINGH RATHORE

doi:10.46753/pjaa.2018.v05i02(i).003

NEAR EXACT OPERATOR BANACH FRAMES IN BANACH SPACES

Poincare Journal of Analysis and Applications ◽

10.46753/pjaa.2019.v06i01.006 ◽

2019 ◽

Vol 06 (01) ◽

pp. 67-75

Author(s):

SHALU SHARMA ◽

KHOLE TIMOTHY POUMAI ◽

CHANDER SHEKHAR

Keyword(s):

Banach Spaces ◽

Banach Frames

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On Perturbation of Weighted G−Banach Frames in Banach Spaces

Journal of the Indian Mathematical Society ◽

10.18311/jims/2020/21297 ◽

2020 ◽

Vol 87 (1-2) ◽

pp. 114

Author(s):

Ghanshyam Singh Rathore ◽

Tripti Mittal

Keyword(s):

Finite Number ◽

Banach Spaces ◽

Sufficient Conditions ◽

Bessel Sequence ◽

Banach Frames ◽

Banach Frame

In the present paper, we study perturbation of weighted g−Banach frames in Banach spaces and obtain perturbation results for weighted g−Banach frames. Also, sufficient conditions for the perturbation of weighted g−Banach frames by positively confined sequence of scalars and uniformly scaled version of a given weighted g−Banach Bessel sequence have been given. Finally, we give a condition under which the sum of finite number of sequences of operators is a weighted g−Banach frame by comparing each of the sequences with another system of weighted g−Banach frames in Banach spaces.

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ON BI-BANACH FRAMES IN BANACH SPACES

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691314500155 ◽

2014 ◽

Vol 12 (02) ◽

pp. 1450015 ◽

Cited By ~ 1

Author(s):

SHALU SHARMA

Keyword(s):

Banach Space ◽

Banach Spaces ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Banach Frames ◽

Banach Frame ◽

Necessary And Sufficient

Bi-Banach frames in Banach spaces have been defined and studied. A necessary and sufficient condition under which a Banach space has a Bi-Banach frame has been given. Finally, Pseudo exact retro Banach frames have been defined and studied.

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

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691314500246 ◽

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.

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On fusion frames in Banach spaces

Georgian Mathematical Journal ◽

10.1515/gmj.2010.029 ◽

2010 ◽

Vol 18 (1) ◽

pp. 121-130

Author(s):

Shiv K. Kaushik ◽

Varinder Kumar

Keyword(s):

Banach Spaces ◽

Complete Sequence ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Banach Frames ◽

Fusion Frames ◽

Banach Frame ◽

Necessary And Sufficient

Abstract A necessary and sufficient condition for a complete sequence of subspaces to be a fusion Banach frame for E is given. Also, we introduce fusion Banach frame sequences and give a characterization for a complete sequence of subspaces of E to be a fusion Banach frame for E in terms of fusion Banach frame sequences. Finally, along with other results, we characterize fusion Banach frames in terms of Banach frames.

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ON NEAR EXACT BANACH FRAMES IN BANACH SPACES

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972708000889 ◽

2008 ◽

Vol 78 (2) ◽

pp. 335-342 ◽

Cited By ~ 2

Author(s):

P. K. JAIN ◽

S. K. KAUSHIK ◽

NISHA GUPTA

Keyword(s):

Banach Spaces ◽

Product Space ◽

Sufficient Condition ◽

Banach Frames ◽

Banach Frame

AbstractNear exact Banach frames are introduced and studied, and examples demonstrating the existence of near exact Banach frames are given. Also, a sufficient condition for a Banach frame to be near exact is obtained. Further, we consider block perturbation of retro Banach frames, and prove that a block perturbation of a retro Banach frame is also a retro Banach frame. Finally, it is proved that if E and F are both Banach spaces having Banach frames, then the product space E×F has an exact Banach frame.

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