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M-weak and L-weak compactness of b-weakly compact operators

J. H'Michane, A. El Kaddouri, K. Bouras, M. Moussa (2013)

Commentationes Mathematicae Universitatis Carolinae

We characterize Banach lattices under which each b-weakly compact (resp. b-AM-compact, strong type (B)) operator is L-weakly compact (resp. M-weakly compact).

On a weak Freudenthal spectral theorem

Marek Wójtowicz (1992)

Commentationes Mathematicae Universitatis Carolinae

Let X be an Archimedean Riesz space and 𝒫 ( X ) its Boolean algebra of all band projections, and put 𝒫 e = { P e : P 𝒫 ( X ) } and e = { x X : x ( e - x ) = 0 } , e X + . X is said to have Weak Freudenthal Property ( WFP ) provided that for every e X + the lattice l i n 𝒫 e is order dense in the principal band e d d . This notion is compared with strong and weak forms of Freudenthal spectral theorem in Archimedean Riesz spaces, studied by Veksler and Lavrič, respectively. WFP is equivalent to X + -denseness of 𝒫 e in e for every e X + , and every Riesz space with sufficiently many projections...

On algebra homomorphisms in complex almost f -algebras

Abdelmajid Triki (2002)

Commentationes Mathematicae Universitatis Carolinae

Extensions of order bounded linear operators on an Archimedean vector lattice to its relatively uniform completion are considered and are applied to show that the multiplication in an Archimedean lattice ordered algebra can be extended, in a unique way, to its relatively uniform completion. This is applied to show, among other things, that any order bounded algebra homomorphism on a complex Archimedean almost f -algebra is a lattice homomorphism.

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