On orthomorphisms, quasi-orthomorphisms and quasi-multipliers
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.313, sa.1, ss.120-131, 2006 (SCI-Expanded, Scopus)
- 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.