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2017•Archiv der MathematikOpen access

L-weakly and M-weakly compact operators and the centre

Erdal Bayram, A. W. Wickstead

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Abstract

We extend known results concerning the centre of spaces of regular (resp. weakly compact or compact) operators between two Banach lattices to the setting of L-weakly compact and M-weakly compact operators. We also show that the L-weakly compact, M-weakly compact, and compact operators lying in the centre of a Banach lattice coincide.

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What this paper is about

We extend known results concerning the centre of spaces of regular (resp. weakly compact or compact) operators between two Banach lattices to the setting of L-weakly compact and M-weakly compact operators. We also show that the L-weakly compact, M-weakly compact, and compact operators lying in the centre of a Banach lattice coincide.

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Available abstract

We extend known results concerning the centre of spaces of regular (resp. weakly compact or compact) operators between two Banach lattices to the setting of L-weakly compact and M-weakly compact operators. We also show that the L-weakly compact, M-weakly compact, and compact operators lying in the centre of a Banach lattice coincide.

Key concepts: Mathematics, Compact operator on Hilbert space, Compact operator, Locally compact space, Compact space, Pure mathematics, Relatively compact subspace, Banach space

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