On some geometric properties of generalized Musielak-Orlicz sequence space and corresponding operator ideals

Amit Maji; P. D. Srivastava

doi:10.15352/bjma/09-4-2

2015 On some geometric properties of generalized Musielak-Orlicz sequence space and corresponding operator ideals

Amit Maji, P. D. Srivastava

Banach J. Math. Anal. 9(4): 14-33 (2015). DOI: 10.15352/bjma/09-4-2

Abstract

Let ${\Phi} =(\phi_n)$ be a Musielak-Orlicz function, $X$ be a real Banach space and $A$ be any infinite matrix. In this paper, a generalized vector-valued Musielak-Orlicz sequence space $l_{{\Phi}}^{A}(X)$ is introduced. It is shown that the space is a complete normed linear space under certain conditions on the matrix $A$. It is also shown that $l_{{\Phi}}^{A}(X)$ is a $\sigma$-Dedekind complete whenever $X$ is so. We have discussed some geometric properties, namely, uniformly monotone, uniform Opial property for this space. Using the sequence of $s$-number (in the sense of Pietsch), the operators of $s$-type $l_{{\Phi}}^{A}$ and operator ideals under certain conditions on the matrix $A$ are discussed.

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Amit Maji and P. D. Srivastava "On some geometric properties of generalized Musielak-Orlicz sequence space and corresponding operator ideals," Banach Journal of Mathematical Analysis 9(4), 14-33, (2015). https://doi.org/10.15352/bjma/09-4-2

Published: 2015

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