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arXiv · 2207.11105

Operators whose adjoints and second adjoints are almost Dunford-Pettis

Geraldo Botelho·Luis Alberto Garcia
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Abstract

First we characterize the Banach lattices E whose biduals have the positive Schur property by means of second adjoints of operators on E being almost Dunford-Pettis. Next we extend some known results concerning conditions on the Banach lattices E and F under which the adjoint T* and the second adjoint T** of any positive almost Dunford-Pettis operator T from E to F are almost Dunford-Pettis. Finally, we prove when T* and T** are almost Dunford-Pettis for any (non necessarily almost Dunford-Pettis) T that is either bounded, regular, order bounded or weakly compact.

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Geraldo Botelho, Luis Alberto Garcia. 2024-09-30. Operators whose adjoints and second adjoints are almost Dunford-Pettis. https://arxiv.org/abs/2207.11105

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