- Title
- An extension of a non-commutative Choquet-Deny Theorem
- Creator
- Willis, G. A.
- 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
- Publisher
- American Mathematical Society
- Resource Type
- journal article
- Date
- 2000
- 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 TN : ℓ¹(G) → ℓ¹(G/N). It is shown that the kernel of this map may be decomposed as ker(TN) = 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 TN(I) is closed in ℓ¹(G/N). This answers a question of Reiter.
- Subject
- group algebra; Choquet-Deny Theorem; group theory
- Identifier
- http://hdl.handle.net/1959.13/933451
- Identifier
- uon:11616
- Identifier
- ISSN:0002-9939
- Rights
- First published in Proceedings of the American Mathematical Society in Volume 128, Number 1, 2000 published by the American Mathematical Society.
- Language
- eng
- Full Text
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