On invariant subalgebras of the Fourier-Stieltjes algebra of a locally compact group

Bekka, Mohammed E. B.; Lau, Anthony To-Ming; Schlichting, Günter

doi:10.1007/bf01934339

Cited by 26 publications

(25 citation statements)

References 12 publications

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“…These results provide new characterizations of amenable and inner amenable locally compact groups, as well as amenable action on coset spaces. Coefficient subspaces of the Fourier-Stieltjes algebra have been studied by several authors, see for example [1], [4], [6], [7], [9], and [13].…”

Section: Introductionmentioning

confidence: 99%

Amenable representations and coefficient subspaces of Fourier-Stieltjes algebras

Stokke¹

2006

MATH. SCAND.

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Amenable unitary representations of a locally compact group, G, are studied in terms of associated coefficient subspaces of the Fourier-Stieltjes algebra B(G), and in terms of the existence of invariant and multiplicative states on associated von Neumann and C * -algebras. We introduce Fourier algebras and reduced Fourier-Stieltjes algebras associated to arbitrary representations, and study amenable representations in relation to these algebras.

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Section: Introductionmentioning

confidence: 99%

Amenable representations and coefficient subspaces of Fourier-Stieltjes algebras

Stokke¹

2006

MATH. SCAND.

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“…As is well known A(G) is weak*-dense in B(G) if and only if G is amenable. In [3] translation invariant *-subalgebras A of B(G) were studied, and it was shown that if such A is weak*-closed and point separating, then it must contain A(G). However, apart from this, very little seems to be known about weak*-closed subspaces of B(G).…”

Section: Introductionmentioning

confidence: 99%

Weak-closedness of subspaces of Fourier-Stieltjes algebras and weak-continuity of the restriction map

Bekka

Kaniuth

Lau

et al. 1998

Trans. Amer. Math. Soc.

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“…As already noted, an open subgroup H determines a non-zero, invariant C * -subalgebra X of C * (G) via (2). Obviously x∈X supp x ⊆ H and the converse follows easily because H is open.…”

Section: Theorem 14mentioning

confidence: 81%

Compact quantum subgroups and left invariant C⁎-subalgebras of locally compact quantum groups

Salmi

2011

Journal of Functional Analysis

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We show that there is a one-to-one correspondence between compact quantum subgroups of a coamenable locally compact quantum group G and certain left invariant C * -subalgebras of C 0 (G). We also prove that every compact quantum subgroup of a co-amenable quantum group is co-amenable. Moreover, there is a one-to-one correspondence between open subgroups of an amenable locally compact group G and non-zero, invariant C * -subalgebras of the group C * -algebra C * r (G).

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On invariant subalgebras of the Fourier-Stieltjes algebra of a locally compact group

Cited by 26 publications

References 12 publications

Amenable representations and coefficient subspaces of Fourier-Stieltjes algebras

Amenable representations and coefficient subspaces of Fourier-Stieltjes algebras

Weak-closedness of subspaces of Fourier-Stieltjes algebras and weak-continuity of the restriction map

Compact quantum subgroups and left invariant C⁎-subalgebras of locally compact quantum groups

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On invariant subalgebras of the Fourier-Stieltjes algebra of a locally compact group

Cited by 26 publications

References 12 publications

Amenable representations and coefficient subspaces of Fourier-Stieltjes algebras

Amenable representations and coefficient subspaces of Fourier-Stieltjes algebras

Weak*-closedness of subspaces of Fourier-Stieltjes algebras and weak*-continuity of the restriction map

Compact quantum subgroups and left invariant C⁎-subalgebras of locally compact quantum groups

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Product

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Weak-closedness of subspaces of Fourier-Stieltjes algebras and weak-continuity of the restriction map