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arXiv · 2008.08491

Characterization of $M$-compact sets via statistically convergent sequences

Susmita Seal·Sumit Som·Sudeshna Basu·Lakshmi Kanta Dey
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Abstract

In this paper, we study stability of $M$-compactness for $l^p$ sum of Banach spaces for $1\leq p<\infty$. We also obtain a characterization of $M$-compact sets in terms of statistically maximizing sequence, a notion which is weaker than a maximizing sequence. Moreover, we introduce the notion of $\mathcal{I}$-$M$-compactness of a bounded subset $M$ of a normed linear space $X$ with respect to an ideal $\mathcal{I}$ and show that it is equivalent to $M$-compactness for non-trivial admissible ideals.

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Susmita Seal, Sumit Som, Sudeshna Basu, Lakshmi Kanta Dey. 2020-08-19. Characterization of $M$-compact sets via statistically convergent sequences. https://arxiv.org/abs/2008.08491

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