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2013 $(X_{d}, X_{d}^{*})$-Bessel multipliers in Banach spaces
Mohammad Hasan Faroughi , Elnaz Osgooei , Asghar Rahimi
Banach J. Math. Anal. 7(2): 146-161 (2013). DOI: 10.15352/bjma/1363784228

Abstract

Multipliers have recently been introduced as operators for Bessel sequences and frames in Hilbert spaces. In this paper, we define the concept of $(X_{d}, X_{d}^{*})$ and $(l^{\infty}, X_{d}, X_{d}^{*})$-Bessel multipliers in Banach spaces and investigate the compactness of these multipliers. Also, we study the possibility of invertibility of $(l^{\infty}, X_{d}, X_{d}^{*})$-Bessel multiplier depending on the properties of its corresponding sequences and its symbol. Furthermore, we prove that every $(X_{d}, X_{d}^{*})$-Bessel multiplier is a $\lambda$-nuclear operator.

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Mohammad Hasan Faroughi . Elnaz Osgooei . Asghar Rahimi . "$(X_{d}, X_{d}^{*})$-Bessel multipliers in Banach spaces." Banach J. Math. Anal. 7 (2) 146 - 161, 2013. https://doi.org/10.15352/bjma/1363784228

Information

Published: 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1266.42083
MathSciNet: MR3039944
Digital Object Identifier: 10.15352/bjma/1363784228

Subjects:
Primary: ‎42C40
Secondary: 41A58 , 42C15 , 47B99

Keywords: $\lambda$-nuclear operator , $X_{d}$-Bessel sequence , ($X_{d}, X_{d}^{*}$)-Bessel multiplier

Rights: Copyright © 2013 Tusi Mathematical Research Group

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Vol.7 • No. 2 • 2013
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