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Displaying similar documents to “Disjointness preserving and diffuse operators”

The band generated by homomorphisms on Banach lattices.

David C. Carothers, William A. Feldman (1998)

Extracta Mathematicae

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This paper will consider the closure of the set of operators which may be expressed as a sum of lattice homomorphisms whose range is contained in a Dedekind complete Banch lattice.

The order σ -complete vector lattice of AM-compact operators

Belmesnaoui Aqzzouz, Redouane Nouira (2009)

Czechoslovak Mathematical Journal

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We establish necessary and sufficient conditions under which the linear span of positive AM-compact operators (in the sense of Fremlin) from a Banach lattice E into a Banach lattice F is an order σ -complete vector lattice.

A disjointness type property of conditional expectation operators

Beata Randrianantoanina (2005)

Colloquium Mathematicae

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We give a characterization of conditional expectation operators through a disjointness type property similar to band-preserving operators. We say that the operator T:X→ X on a Banach lattice X is semi-band-preserving if and only if for all f, g ∈ X, f ⊥ Tg implies that Tf ⊥ Tg. We prove that when X is a purely atomic Banach lattice, then an operator T on X is a weighted conditional expectation operator if and only if T is semi-band-preserving.