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When a lattice homomorphism is a Riesz homomorphism

✍ Scribed by Z. Ercan; A.W. Wickstead

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
87 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let E and F be uniformly complete vector lattices with disjoint complete systems (u~i~ )~i ∈I~ and (v~i~ )~i ∈I~ of projection elements of E and F respectively. In this paper we prove that if T is a lattice homomorphism from E into F with T (Ξ»u~i~ ) = Ξ»v~i~ for each Ξ» ∈ ℝ and i ∈ I then T is linear. This generalizes the main results of [4] and [5]. (Β© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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