On the sequence spaces involving bell numbers

Abstract

In the present paper, we introduce a new regular matrix $\tilde{B}$ and define the sequence space ${\ell }_p(\tilde{B})$. We also examine some topological properties for this space and determine $\alpha \text{ - },\beta \text{ - },\gamma \text{ - }$duals. As well, we characterize some matrix classes and investigate some geometric properties such as uniform convexity, strict convexity and super-reflexivity.

KEYWORDS:

• Bell numbers
• sequence space
• matrix transformations
• $\alpha \text{ - },\beta \text{ - },\gamma \text{ - }$ duals
• geometric properties

MSC codes:

• 11B73
• 46A45
• 46B20
• 46B45

Disclosure statement

No potential conflict of interest was reported by the author(s).