Group representations with empty residual spectrum

Choi, Yemon (2010) Group representations with empty residual spectrum. Integral Equations and Operator Theory, 67 (1). pp. 95-107. ISSN 1420-8989

Full text not available from this repository.

Abstract

Let X be a Banach space on which a discrete group Γ acts by isometries. For certain natural choices of X, every element of the group algebra, when regarded as an operator on X, has empty residual spectrum. We show, for instance, that this occurs if X is ℓ 2(Γ) or the group von Neumann algebra VN(Γ). In our approach, we introduce the notion of a surjunctive pair, and develop some of the basic properties of this construction. The cases X = ℓ p (Γ) for 1 ≤ p < 2 or 2 < p < ∞ are more difficult. If Γ is amenable we can obtain partial results, using a majorization result of Herz; an example of Willis shows that some condition on Γ is necessary.

Item Type:
Journal Article
Journal or Publication Title:
Integral Equations and Operator Theory
Additional Information:
Erratum: Int. Eq. Op. Th. 69 (2011), no. 1, 149--150. DOI: 10.1007/s00020-010-1847-y
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2602
Subjects:
?? residual spectrum surjunctive group von neumann algebra directly finiteamenable groupalgebra and number theoryanalysis ??
ID Code:
68301
Deposited By:
Deposited On:
24 Jan 2014 05:52
Refereed?:
Yes
Published?:
Published
Last Modified:
15 Jul 2024 14:28