Sets of uniqueness on noncommutative locally compact groups. II
Marek Bożejko (1979)
Colloquium Mathematicae
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Marek Bożejko (1979)
Colloquium Mathematicae
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M.E. Bekka, A.T. Lau, G. Schlichting (1992)
Mathematische Annalen
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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.
Eberhard Kaniuth (1994)
Mathematica Scandinavica
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Erik Svensson (1980)
Mathematica Scandinavica
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Juan J. Font (1998)
Colloquium Mathematicae
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Horst Leptin (1987)
Colloquium Mathematicae
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Brian E. Forrest, Ebrahim Samei, Nico Spronk (2010)
Studia Mathematica
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We study two related questions. (1) For a compact group G, what are the ranges of the convolution maps on A(G × G) given for u,v in A(G) by u × v ↦ u*v̌ (v̌(s) = v(s^-1)) and u × v ↦ u*v? (2) For a locally compact group G and a compact subgroup K, what are the amenability properties of the Fourier algebra of the coset space A(G/K)? The algebra A(G/K) was defined and studied by the first named author. In answering the first question, we obtain, for compact groups which...
John J. F. Fournier (1985)
Colloquium Mathematicae
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J. Florek (1987)
Colloquium Mathematicae
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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).
Michael Yin-hei Cheng (2011)
Studia Mathematica
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Let G be a locally compact group, G* be the set of all extreme points of the set of normalized continuous positive definite functions of G, and a(G) be the closed subalgebra generated by G* in B(G). When G is abelian, G* is the set of Dirac measures of the dual group Ĝ, and a(G) can be identified as l¹(Ĝ). We study the properties of a(G), particularly its spectrum and its dual von Neumann algebra.
Roger Andersson (1980)
Mathematica Scandinavica
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Martin Blümlinger (1991)
Mathematische Annalen
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Krishnan Parthasarathy, Nageswaran Shravan Kumar (2011)
Studia Mathematica
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Ditkin sets for the Fourier algebra A(G/K), where K is a compact subgroup of a locally compact group G, are studied. The main results discussed are injection theorems, direct image theorems and the relation between Ditkin sets and operator Ditkin sets and, in the compact case, the inverse projection theorem for strong Ditkin sets and the relation between strong Ditkin sets for the Fourier algebra and the Varopoulos algebra. Results on unions of Ditkin sets and on tensor products are...
Jean de Cannière, Wolfgang Arendt (1983)
Mathematische Annalen
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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.
Keith F. Taylor (1983)
Mathematische Annalen
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María L. Torres de Squire (1993)
Publicacions Matemàtiques
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We extend to locally compact abelian groups, Fejer's theorem on pointwise convergence of the Fourier transform. We prove that lim φ * f(y) = f (y) almost everywhere for any function f in the space (L, l)(G) (hence in L(G)), 2 ≤ p ≤ ∞, where {φ} is Simon's generalization to locally compact abelian groups of the summability Fejer Kernel. Using this result, we extend to locally compact abelian groups a theorem of F. Holland on the Fourier transform of unbounded measures of type q. ...