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2010•Mathematical Proceedings of the Royal Irish AcademyRequires access

THE SCHUR PROPERTY OF BANACH LATTICES AND THE COMPACTNESS OF WEAKLY COMPACT OPERATORS

Belmesnaoui Aqzzouz, Aziz Elbour

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Abstract

We establish some characterizations of the Schur property (resp. positive Schur property) of Banach lattices by the compactness (resp. L-weak compactness, M-weak compactness) of weakly compact (resp. positive weakly compact) operators.

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What this paper is about

We establish some characterizations of the Schur property (resp. positive Schur property) of Banach lattices by the compactness (resp. L-weak compactness, M-weak compactness) of weakly compact (resp. positive weakly compact) operators.

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Available abstract

We establish some characterizations of the Schur property (resp. positive Schur property) of Banach lattices by the compactness (resp. L-weak compactness, M-weak compactness) of weakly compact (resp. positive weakly compact) operators.

Key concepts: Compact space, Approximation property, Mathematics, Property (philosophy), Schur's theorem, Pure mathematics, Compact operator, Eberlein–Šmulian theorem

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