When a lattice homomorphism is a Riesz homomorphism

Ercan Z., Wickstead A. W.

MATHEMATISCHE NACHRICHTEN, vol.279, pp.1024-1027, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 279
  • Publication Date: 2006
  • Doi Number: 10.1002/mana.200410408
  • Journal Name: MATHEMATISCHE NACHRICHTEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1024-1027
  • Middle East Technical University Affiliated: No

Abstract

Let E and F be uniformly complete vector lattices with disjoint complete systems (u(i))(i is an element of I) and (v(i))(i is an element of 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(lambda u(i)) = lambda v(i) for each lambda is an element of R and i is an element of I then T is linear. This generalizes the main results of [4] and [5]. (C) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.