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IDEALS IN OPERATOR SPACE PROJECTIVE TENSOR PRODUCT OF C*-ALGEBRAS

Part of: Selfadjoint operator algebras Linear spaces and algebras of operators

Published online by Cambridge University Press:  18 November 2011

RANJANA JAIN  and
AJAY KUMAR
RANJANA JAIN
Affiliation:
Department of Mathematics, Lady Shri Ram College for Women, New Delhi-110024, India (email: [email protected])
AJAY KUMAR*
Affiliation:
Department of Mathematics, University of Delhi, Delhi-110007, India (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Let A and B be C*-algebras. We prove the slice map conjecture for ideals in the operator space projective tensor product . As an application, a characterization of the prime ideals in the Banach *-algebra is obtained. In addition, we study the primitive ideals, modular ideals and the maximal modular ideals of . We also show that the Banach *-algebra possesses the Wiener property and that, for a subhomogeneous C*-algebra A, the Banach * -algebra is symmetric.

Keywords

C*-algebrasoperator space projective tensor normHaagerup tensor product

MSC classification

Secondary: 46L06: Tensor products of $C^*$-algebras 47L25: Operator spaces (= matricially normed spaces)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 2 , October 2011 , pp. 275 - 288
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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