Banach Journal of Mathematical Analysis

$(X_{d}, X_{d}^{*})$-Bessel multipliers in Banach spaces

Mohammad Hasan Faroughi , Elnaz Osgooei , and Asghar Rahimi

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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.

Article information

Banach J. Math. Anal., Volume 7, Number 2 (2013), 146 -161 .

First available in Project Euclid: 20 March 2013

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Zentralblatt MATH identifier

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

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


Faroughi , Mohammad Hasan; Osgooei , Elnaz; Rahimi , Asghar. $(X_{d}, X_{d}^{*})$-Bessel multipliers in Banach spaces. Banach J. Math. Anal. 7 (2013), no. 2, 146 --161. doi:10.15352/bjma/1363784228.

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