Norms of inner derivations for multiplier algebras of C*-algebras and group C*-algebras

Robert J Archbold; Eberhard Kaniuth; Douglas W B Somerset

doi:10.1016/j.jfa.2011.12.015

Norms of inner derivations for multiplier algebras of C-algebras and group C-algebras

Robert J Archbold, Eberhard Kaniuth, Douglas W B Somerset

Mathematical Science

Paderborn University

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

The derivation constant K (A) ≥ 1/2 has been previously studied for unital non-commutative C*- algebras A. This paper begins the study of K(M(A)) where M (A) is the multiplier algebra of a non-unital C*-algebra A. Two results are obtained giving separate conditions on A which imply that K(M(A)) ≤ 1.These results are applied to A=C* (G)for a number of locally compact groups G including SL(2,R), SL (2,C)and several 2-step solvable groups. In these cases, K (M(A))=1. On the other hand, if G is a (non-abelian) amenable [SIN]-group then K (M(A))=1/2.

Original language	English
Pages (from-to)	2050-2073
Number of pages	24
Journal	Journal of Functional Analysis
Volume	262
Issue number	5
Early online date	29 Dec 2011
DOIs	https://doi.org/10.1016/j.jfa.2011.12.015
Publication status	Published - 1 Mar 2012

Bibliographical note

Acknowledegments
The authors are grateful to the London Mathematical Society for grant number 4919 which partially supported this research.

Keywords

C⁎-algebra
multiplier algebra
inner derivation
norm
ideal space and topology
graph structure
locally compact group
Group C⁎-algebra

Access to Document

10.1016/j.jfa.2011.12.015Licence: Other

Cite this

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title = "Norms of inner derivations for multiplier algebras of C*-algebras and group C*-algebras",

abstract = "The derivation constant K (A) ≥ 1/2 has been previously studied for unital non-commutative C*- algebras A. This paper begins the study of K(M(A)) where M (A) is the multiplier algebra of a non-unital C*-algebra A. Two results are obtained giving separate conditions on A which imply that K(M(A)) ≤ 1.These results are applied to A=C* (G)for a number of locally compact groups G including SL(2,R), SL (2,C)and several 2-step solvable groups. In these cases, K (M(A))=1. On the other hand, if G is a (non-abelian) amenable [SIN]-group then K (M(A))=1/2.",

keywords = "C⁎-algebra, multiplier algebra, inner derivation, norm, ideal space and topology, graph structure, locally compact group, Group C⁎-algebra",

author = "Archbold, {Robert J} and Eberhard Kaniuth and Somerset, {Douglas W B}",

note = "Acknowledegments The authors are grateful to the London Mathematical Society for grant number 4919 which partially supported this research.",

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doi = "10.1016/j.jfa.2011.12.015",

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T1 - Norms of inner derivations for multiplier algebras of C*-algebras and group C*-algebras

AU - Archbold, Robert J

AU - Kaniuth, Eberhard

AU - Somerset, Douglas W B

N1 - Acknowledegments The authors are grateful to the London Mathematical Society for grant number 4919 which partially supported this research.

PY - 2012/3/1

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N2 - The derivation constant K (A) ≥ 1/2 has been previously studied for unital non-commutative C*- algebras A. This paper begins the study of K(M(A)) where M (A) is the multiplier algebra of a non-unital C*-algebra A. Two results are obtained giving separate conditions on A which imply that K(M(A)) ≤ 1.These results are applied to A=C* (G)for a number of locally compact groups G including SL(2,R), SL (2,C)and several 2-step solvable groups. In these cases, K (M(A))=1. On the other hand, if G is a (non-abelian) amenable [SIN]-group then K (M(A))=1/2.

AB - The derivation constant K (A) ≥ 1/2 has been previously studied for unital non-commutative C*- algebras A. This paper begins the study of K(M(A)) where M (A) is the multiplier algebra of a non-unital C*-algebra A. Two results are obtained giving separate conditions on A which imply that K(M(A)) ≤ 1.These results are applied to A=C* (G)for a number of locally compact groups G including SL(2,R), SL (2,C)and several 2-step solvable groups. In these cases, K (M(A))=1. On the other hand, if G is a (non-abelian) amenable [SIN]-group then K (M(A))=1/2.

KW - C⁎-algebra

KW - multiplier algebra

KW - inner derivation

KW - norm

KW - ideal space and topology

KW - graph structure

KW - locally compact group

KW - Group C⁎-algebra

U2 - 10.1016/j.jfa.2011.12.015

DO - 10.1016/j.jfa.2011.12.015

M3 - Article

SN - 0022-1236

VL - 262

SP - 2050

EP - 2073

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 5

ER -