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CLOSED IDEALS AND LIE IDEALS OF MINIMAL TENSOR PRODUCT OF CERTAIN C*-ALGEBRAS

Part of: Selfadjoint operator algebras Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  03 July 2020

BHARAT TALWAR  and
RANJANA JAIN
BHARAT TALWAR
Affiliation:
Department of Mathematics, University of Delhi, Delhi, 110007, India, e-mails: btalwar.math@gmail.com, rjain@maths.du.ac.in
RANJANA JAIN
Affiliation:
Department of Mathematics, University of Delhi, Delhi, 110007, India, e-mails: btalwar.math@gmail.com, rjain@maths.du.ac.in
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Abstract

For a locally compact Hausdorff space X and a C*-algebra A with only finitely many closed ideals, we discuss a characterization of closed ideals of C0(X,A) in terms of closed ideals of A and a class of closed subspaces of X. We further use this result to prove that a closed ideal of C0(X)⊗min A is a finite sum of product ideals. We also establish that for a unital C*-algebra A, C0(X,A) has the centre-quotient property if and only if A has the centre-quotient property. As an application, we characterize the closed Lie ideals of C0(X,A) and identify all the closed Lie ideals of HC0(X)⊗minB(H), H being a separable Hilbert space.

MSC classification

Primary: 46L06: Tensor products of $C^*$-algebras
Secondary: 17B05: Structure theory

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 2 , May 2021 , pp. 414 - 425
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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