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.
Banach J. Math. Anal.
7(2):
146-161
(2013).
DOI: 10.15352/bjma/1363784228