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

Tom 183 / 2007

E. Kaniuth, A. T. Lau, A. Ülger Studia Mathematica 183 (2007), 35-62 MSC: Primary 46J05, 46J20, 43A30, 43A40. DOI: 10.4064/sm183-1-3


Let $A$ and $B$ be semisimple commutative Banach algebras with bounded approximate identities. We investigate the problem of extending a homomorphism $\varphi : A \to B$ 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 $\varphi $) 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.


  • E. KaniuthInstitut für Mathematik
    Universität Paderborn
    D-33095 Paderborn, Germany
  • A. T. LauDepartment of Mathematical and Statistical Sciences
    University of Alberta
    Edmonton, Alberta, Canada T6G 2G1
  • A. ÜlgerDepartment of Mathematics
    Koc University
    34450 Sariyer, Istanbul, Turkey

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