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arXiv · 2309.03775

Disjoint $p$-convergent operators and their adjoints

Geraldo Botelho·Luis Alberto Garcia·Vinícius C. C. Miranda
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Abstract

First we give conditions on a Banach lattice $E$ so that an operator $T$ from $E$ to any Banach space is disjoint $p$-convergent if and only if $T$ is almost Dunford-Pettis. Then we study when adjoints of positive operators between Banach lattices are disjoint $p$-convergent. For instance, we prove that the following conditions are equivalent for all Banach lattices $E$ and $F$: (i) A positive operator $T \colon E \to F$ is almost weak $p$-convergent if and only if $T^*$ is disjoint $p$-convergent; (ii) $E^*$ has order continuous norm or $F^*$ has the positive Schur property of order $p$. Very recent results are improved, examples are given and applications of the main results are provided.

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Geraldo Botelho, Luis Alberto Garcia, Vinícius C. C. Miranda. 2023-09-20. Disjoint $p$-convergent operators and their adjoints. https://arxiv.org/abs/2309.03775

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