Separation properties in the primitive ideal space of a multiplier algebra

Robert J Archbold, Douglas W. B. Somerset

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Abstract

We use recent work on spectral synthesis in multiplier algebras to give an intrinsic characterization of the separable C*-algebras A for which Orc(M(A)) = 1, i.e., for which the relation of inseparability on the topological space of primitive ideals of the multiplier algebra M(A) is an equivalence relation. This characterization has applications to the calculation of norms of inner derivations and other elementary operators on A and M(A). For example, we give necessary and sufficient conditions on the ideal structure of a separable C*-algebra A for the norm of every inner derivation to be twice the distance of the implementing element to the centre of M(A).
Original languageEnglish
Pages (from-to)389-418
Number of pages30
JournalIsrael Journal of Mathematics
Volume200
Issue number1
Early online date7 Feb 2014
DOIs
Publication statusPublished - Jun 2014

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Inner Derivation
Multiplier Algebra
Primitive Ideal
Separation Property
C*-algebra
Elementary Operators
Spectral Synthesis
Norm
Equivalence relation
Topological space
Necessary Conditions
Sufficient Conditions

Cite this

Separation properties in the primitive ideal space of a multiplier algebra. / Archbold, Robert J; Somerset, Douglas W. B.

In: Israel Journal of Mathematics, Vol. 200, No. 1, 06.2014, p. 389-418.

Research output: Contribution to journalArticle

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