Extensions and isomorphisms for the generalized Fourier algebras of a locally compact group

Monfared, M. Sangani

doi:10.1016/s0022-1236(02)00040-x

Cited by 22 publications

(14 citation statements)

References 30 publications

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“…[1], [2] or [6]), on spaces of continuous functions (see e.g. [14], [3], [7], [15] or [12]), on group algebras of locally compact Abelian groups ( [8]), on Fourier algebras ( [10] and [20]) and on some others (see e.g. [16], [17] or [5]).…”

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confidence: 99%

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Disjointness preserving mappings on BSE Ditkin algebras

Font¹

2011

Publ. Math. Debrecen

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Let A and B be regular Banach function algebras. A linear map T defined from A into B is said to be disjointness preserving or sepa-We prove that if there exists a disjointness preserving bijection between two BSE Ditkin algebras with a BAI, then they are isomorphic as algebras. As a corollary we can deduce that two of these algebras are algebraically isomorphic if there exists a surjective isometry between them for the supremum norm.

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confidence: 99%

“…A similar result was obtained in [10] (resp. [20]) for Fourier algebras (resp. generalized Fourier algebras) of amenable locally compact groups.…”

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confidence: 99%

Disjointness preserving mappings on BSE Ditkin algebras

Font¹

2011

Publ. Math. Debrecen

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“…The same is true for the group algebras of locally compact groups (see, e.g., [22,23,20,45]). Let G be a locally compact group.…”

Section: Introductionmentioning

confidence: 84%

“…Font [19,20] shows that two locally compact amenable groups G 1 and G 2 are homeomorphic if there is a disjointness preserving linear bijection Ψ between the Fourier algebras A(G 1 ) and A(G 2 ). Font's result is proved by Monfared [45], where the amenability condition is replaced with the assumption of boundedness on the linear map. However, neither the induced weight function λ nor the homeomorphism σ respects the group structure.…”

Section: Introductionmentioning

confidence: 99%

Orthogonality and disjointness preserving linear maps between Fourier and Fourier–Stieltjes algebras of locally compact groups

Lau

Wong

2013

Journal of Functional Analysis

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This paper is devoted to the study of orthogonality and disjointness preserving linear maps between Fourier and Fourier-Stieltjes algebras of locally compact groups. We show that a linear bijection Ψ :) between two Fourier algebras (resp. Fourier-Stieltjes algebras) of locally compact groups will induce a topological group isomorphism between G 1 and G 2 , provided that Ψ preserves both disjointness and some kind of orthogonality. This improves earlier results of J. J. Font and M. S. Monfared, where amenability of the groups or continuity of the linear maps are assumed. We also study the structure of bounded and unbounded disjointness preserving linear functionals of Fourier algebras. In the development, general results about disjointness and orthogonality preserving linear maps between C*-algebras, W*-algebras and their preduals are obtained.

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“…The linear maps that preserve the orthogonality, in the sense that they take elements with zero product into elements with zero product, has been extensively studied for group algebras and other Banach algebras associated with a locally compact group [3,6,9,14,15,16,18,19]. This paper focuses on a variety of versions of orthogonality of elements f, g ∈ L 1 (G) of the group algebra of a locally compact group G that are equally likely to occur: It is worth noting that all the aforesaid definitions agree in the case where the group G is abelian.…”

Section: Introductionmentioning

confidence: 99%

Orthogonality preserving linear maps on group algebras

Alaminos¹,

Extremera²,

Villena³

2015

Math. Proc. Camb. Phil. Soc.

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We consider several types of orthogonality conditions on the group algebra L1(G) of a locally compact group G such as f$\ast $g = 0, f$\ast $g☆ = 0, f☆$\ast $g = 0, f$\ast $g = g$\ast $f = 0 and f$\ast $g☆ = g☆$\ast $f = 0, and we describe the linear maps Φ: L1(G) → L1(H) between the group algebras of locally compact groups G and H that take orthogonal functions of L1(G) into orthogonal functions of L1(H). Roughly speaking, they are weighted homomorphisms in the case where we are concerned with the one-sided orthogonality conditions and weighted Jordan homomorphisms in the case where we treat the two-sided orthogonality conditions.

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Extensions and isomorphisms for the generalized Fourier algebras of a locally compact group

Cited by 22 publications

References 30 publications

Disjointness preserving mappings on BSE Ditkin algebras

Disjointness preserving mappings on BSE Ditkin algebras

Orthogonality and disjointness preserving linear maps between Fourier and Fourier–Stieltjes algebras of locally compact groups

Orthogonality preserving linear maps on group algebras

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