Displaying similar documents to “Disjointness preserving mappings between Fourier algebras”

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

E. Kaniuth, A. T. Lau, A. Ülger (2007)

Studia Mathematica

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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...

Contractive homomorphisms of measure algebras and Fourier algebras

Ross Stokke (2012)

Studia Mathematica

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We show that the dual version of our factorization [J. Funct. Anal. 261 (2011)] of contractive homomorphisms φ: L¹(F) → M(G) between group/measure algebras fails to hold in the dual, Fourier/Fourier-Stieltjes algebra, setting. We characterize the contractive w*-w* continuous homomorphisms between measure algebras and (reduced) Fourier-Stieltjes algebras. We consider the problem of describing all contractive homomorphisms φ: L¹(F) → L¹(G).

Real linear isometries between function algebras. II

Osamu Hatori, Takeshi Miura (2013)

Open Mathematics

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We describe the general form of isometries between uniformly closed function algebras on locally compact Hausdorff spaces in a continuation of the study by Miura. We can actually obtain the form on the Shilov boundary, rather than just on the Choquet boundary. We also give an example showing that the form cannot be extended to the whole maximal ideal space.

Amenability of Banach and C*-algebras on locally compact groups

A. Lau, R. Loy, G. Willis (1996)

Studia Mathematica

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Several results are given about the amenability of certain algebras defined by locally compact groups. The algebras include the C*-algebras and von Neumann algebras determined by the representation theory of the group, the Fourier algebra A(G), and various subalgebras of these.

Characterizations of amenable representations of compact groups

Michael Yin-Hei Cheng (2012)

Studia Mathematica

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Let G be a locally compact group and let π be a unitary representation. We study amenability and H-amenability of π in terms of the weak closure of (π ⊗ π)(G) and factorization properties of associated coefficient subspaces (or subalgebras) in B(G). By applying these results, we obtain some new characterizations of amenable groups.

Real-linear isometries between function algebras

Takeshi Miura (2011)

Open Mathematics

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Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → z ∈ ℂ: |z| = 1, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and T f = κ f o φ ¯ on ChB K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not...

Wiener's inversion theorem for a certain class of *-algebras

Tobias Blendek (2014)

Colloquium Mathematicae

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We generalize Wiener's inversion theorem for Fourier transforms on closed subsets of the dual group of a locally compact abelian group to cosets of ideals in a class of non-commutative *-algebras having specified properties, which are all fulfilled in the case of the group algebra of any locally compact abelian group.