Homomorphisms of commutative Banach algebras and extensions to multiplier algebras with applications to Fourier algebras

• Autorzy: E. Kaniuth , A. T. Lau , A. Ülger
• Języki publikacji: EN

Abstrakty

EN

Let A and B be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism φ: A → B to a homomorphism of the multiplier algebras M(A) and M(B) of A and B, respectively. Various sufficient conditions in terms of B (or B and φ) are given that allow the construction of such extensions. We exhibit a number of classes of Banach algebras to which these criteria apply. In addition, we prove a polar decomposition for homomorphisms from A into A with closed range. Our results are applied to Fourier algebras of locally compact groups.

Kategorie tematyczne

• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 46J20: Ideals, maximal ideals, boundaries
• 43A40: Character groups and dual objects
• 46J05: General theory of commutative topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 183
• Numer: 1
• Strony: 35-62

Daty

wydano

2007

Twórcy

autor

E. Kaniuth

• Institut für Mathematik, Universität Paderborn, D-33095 Paderborn, Germany

autor

A. T. Lau

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

autor

A. Ülger

• Department of Mathematics, Koc University, 34450 Sariyer, Istanbul, Turkey

Identyfikatory

DOI

10.4064/sm183-1-3