On the centre of a vector lattice

Chil, Elmiloud; Meyer, Mathieu

doi:10.1016/j.indag.2012.02.003

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Cited by 5 publications

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“…(d) In 1982 A.C. Zaanen [20,Lemma 144.1] modified slightly Luxemburg's proof (b). His arguments show that, for an Archimedean lattice E, we have 0 < T ∈ Orth(E) \ Z (E) if and only if there exists a sequence (v n ) ⊂ E + \ {0} such that T v n ≥ n · v n for every n ∈ N. (e) In 2012 problem (P) was set explicitly by P. Meyer and E. Chil [3,Problem 4]. (f) In 2013 M.A.…”

Section: Introductionmentioning

confidence: 99%

The problem of central orthomorphisms in a class of F-lattices

Wójtowicz

Wiśniewska

2015

Indagationes Mathematicae

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We prove that if an F-lattice E is locally bounded (i.e., an open ball in E centered at 0 is topologically bounded) then every orthomorphism in E is central: Or th(E) = Z (E). This solves partially a problem raised recently by Chil and Meyer.For the Nakano (non-Banach) F-lattice E = ℓ ( p n ) , 0 < p n < 1, the above implication becomes an equivalence.We also study the problem of central orthomorphism in the class of (non-Banach) Musielak-Orlicz sequence spaces ℓ Φ . We give a sufficient condition on Φ for a non-central orthomorphism on ℓ Φ to exist.

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Section: Introductionmentioning

confidence: 99%