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arXiv · 2405.11518

Weakly and weak$^\ast$ $p$-convergent operators

Saak Gabriyelyan
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Abstract

Let $p\in[1,\infty]$. Being motivated by weakly $p$-convergent and weak$^\ast$ $p$-convergent operators between Banach spaces introduced by Fourie and Zeekoei, we introduce and study the classes of weakly $p$-convergent and weak$^\ast$ $p$-convergent operators between arbitrary locally convex spaces. Relationships between these classes of operators are given, and we show that they have ideal properties. Numerous characterizations of weakly $p$-convergent and weak$^\ast$ $p$-convergent operators are given.

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BibTeXRIS

Saak Gabriyelyan. 2024-05-19. Weakly and weak$^\ast$ $p$-convergent operators. https://arxiv.org/abs/2405.11518

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