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CENTRE OF BANACH ALGEBRA VALUED BEURLING ALGEBRAS

Published online by Cambridge University Press:  13 September 2021

BHARAT TALWAR
Affiliation:
Department of Mathematics, University of Delhi, Delhi, India e-mail: [email protected]
RANJANA JAIN*
Affiliation:
Department of Mathematics, University of Delhi, Delhi, India

Abstract

We prove that for a Banach algebra A having a bounded $\mathcal {Z}(A)$ -approximate identity and for every $\mathbf {[IN]}$ group G with a weight w which is either constant on conjugacy classes or satisfies $w \geq 1$ , $\mathcal {Z}(L^{1}_{w}(G) \otimes ^{\gamma } A) \cong \mathcal {Z}(L^{1}_{w}(G)) \otimes ^{\gamma } \mathcal {Z}(A)$ . As an application, we discuss the conditions under which $\mathcal {Z}(L^{1}_{\omega }(G,A))$ enjoys certain Banach algebraic properties, such as weak amenability or semisimplicity.

Type
Research Article
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

Bharat Talwar is supported by a Senior Research Fellowship of CSIR (file number 09/045(1442)/ 2016-EMR-I).

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