2-summing multiplication operators from c₀ (𝒳) into l_p (𝒴)

Abstract

We find the necessary and sufficient conditions for the multiplication operator $M_{\mathcal{V}}:c_0\left(\mathcal{X}\right)\to l_p\left(\mathcal{Y}\right)$ defined by $M_{\mathcal{V}}\left({\left(x_n\right)}_{n\in \mathbb{N}}\right):={\left(V_n\left(x_n\right)\right)}_{n\in \mathbb{N}}$ to be 2-summing. Some examples are given.

Keywords:

• p-summing
• nuclear operators
• operator ideals
• multiplication operator
• vector valued Banach sequence spaces

2020 MSC:

• Primary: 47B10
• 47L20
• Secondary: 46B45

Acknowledgments

We would like to express our gratitude to the referee for his/her careful reading of the manuscript, many valuable comments and suggestions which have improved the final version of the paper.

The author declares that no funds, grants or other support were received during the preparation of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.