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

Robert J Archbold, Eberhard Kaniuth, Douglas W B Somerset

Research output: Contribution to journalArticle

3 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 languageEnglish
Pages (from-to)2050-2073
Number of pages24
JournalJournal of Functional Analysis
Volume262
Issue number5
Early online date29 Dec 2011
DOIs
Publication statusPublished - 1 Mar 2012

Fingerprint

Inner Derivation
Group C*-algebra
Multiplier Algebra
C*-algebra
Norm
Amenable Group
Solvable Group
Locally Compact Group
Unital
Imply

Keywords

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

Cite this

Norms of inner derivations for multiplier algebras of C*-algebras and group C*-algebras. / Archbold, Robert J; Kaniuth, Eberhard; Somerset, Douglas W B.

In: Journal of Functional Analysis, Vol. 262, No. 5, 01.03.2012, p. 2050-2073.

Research output: Contribution to journalArticle

Archbold, Robert J ; Kaniuth, Eberhard ; Somerset, Douglas W B. / Norms of inner derivations for multiplier algebras of C*-algebras and group C*-algebras. In: Journal of Functional Analysis. 2012 ; Vol. 262, No. 5. pp. 2050-2073.
@article{50f7d0056c8f468d8f9e75766946ce8f,
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.",
year = "2012",
month = "3",
day = "1",
doi = "10.1016/j.jfa.2011.12.015",
language = "English",
volume = "262",
pages = "2050--2073",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "5",

}

TY - JOUR

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

Y1 - 2012/3/1

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

VL - 262

SP - 2050

EP - 2073

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 5

ER -