An extension of a non-commutative Choquet-Deny Theorem | NOVA. The University of Newcastle's Digital Repository

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/933451

Title: An extension of a non-commutative Choquet-Deny Theorem
Author/Creator: Willis, G. A.
Description: Let G be a discrete group, and let N be a normal subgroup of G. Then the quotient map G → G/N induces a group algebra homomorphism T_N : ℓ¹(G) → ℓ¹(G/N). It is shown that the kernel of this map may be decomposed as ker(T_N) = R + L, where R is a closed right ideal with a bounded left approximate identity and L is a closed left ideal with a bounded right approximate identity. It follows from this fact that, if I is a closed two-sided ideal in ℓ¹(G), then T_N(I) is closed in ℓ¹(G/N). This answers a question of Reiter.
Relation: Proceedings of the American Mathematical Society Vol. 128, Issue 1, p. 111-118
Relation: http://www.ams.org/journals/proc/2000-128-01/S0002-9939-99-05117-5/#Abstract
Date: 2000
Publisher: American Mathematical Society
Keyword(s): group algebra; Choquet-Deny Theorem; group theory
Resource Type: journal article
Rights: First published in Proceedings of the American Mathematical Society in Volume 128, Number 1, 2000 published by the American Mathematical Society.
Identifier: http://hdl.handle.net/1959.13/933451
Identifier: ISSN:0002-9939
Language: eng

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