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Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

Tom 183 / 2007

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

Streszczenie

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.

Autorzy

• E. KaniuthInstitut für Mathematik
e-mail
• A. T. LauDepartment of Mathematical and Statistical Sciences
University of Alberta