On orthomorphisms, quasi-orthomorphisms and quasi-multipliers

Yilmaz R., Rowlands K.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.313, sa.1, ss.120-131, 2006 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 313 Sayı: 1
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.jmaa.2005.05.074
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.120-131
  • Anahtar Kelimeler: vector lattice, Banach l-algebra, orthomorphisms, quasi-orthomorphisms and quasi-multipliers, ARCHIMEDEAN RIESZ SPACES, F-ALGEBRAS
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Hayır

Özet

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.