Displaying similar documents to “Contractive homomorphisms of measure algebras and Fourier algebras”

Algebrability of the set of non-convergent Fourier series

Richard M. Aron, David Pérez-García, Juan B. Seoane-Sepúlveda (2006)

Studia Mathematica

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We show that, given a set E ⊂ 𝕋 of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t ∈ E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of 𝓒(𝕋) every non-zero element of which has a Fourier series expansion divergent in E.

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...

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.

Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey

Nico Spronk (2010)

Banach Center Publications

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Let G be a locally compact group, and let A(G) and B(G) denote its Fourier and Fourier-Stieltjes algebras. These algebras are dual objects of the group and measure algebras, L - 1 ( G ) and M(G), in a sense which generalizes the Pontryagin duality theorem on abelian groups. We wish to consider the amenability properties of A(G) and B(G) and compare them to such properties for L - 1 ( G ) and M(G). For us, “amenability properties” refers to amenability, weak amenability, and biflatness, as well as some properties...