On orthomorphisms, quasi-orthomorphisms and quasi-multipliers

Yilmaz R., Rowlands K.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.313, no.1, pp.120-131, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 313 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.1016/j.jmaa.2005.05.074
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.120-131
  • Keywords: vector lattice, Banach l-algebra, orthomorphisms, quasi-orthomorphisms and quasi-multipliers, ARCHIMEDEAN RIESZ SPACES, F-ALGEBRAS
  • Recep Tayyip Erdoğan University Affiliated: No

Abstract

In this paper we introduce a new concept, namely that of a quasi-orthomorphism, on a vector lattice, which generalizes the notion of an orthomorphism. We consider quasi-multipliers on l-algebras and establish the relationship between quasi-orthomorphisms and quasi-multipliers. We prove that, for certain Banach algebras, the quasi-orthomorphisms QOrth(A) form a Dedekind complete Banach f-algebra with a multiplicative identity. We conclude with a Kakutani type representation theorem for QOrth(A). (c) 2005 Elsevier Inc. All rights reserved.