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CENTRE OF BANACH ALGEBRA VALUED BEURLING ALGEBRAS

Part of: Methods of category theory in functional analysis Abstract harmonic analysis Locally compact groups and their algebras

Published online by Cambridge University Press:  13 September 2021

BHARAT TALWAR Open the ORCID record for BHARAT TALWAR [Opens in a new window]  and
RANJANA JAIN Open the ORCID record for RANJANA JAIN [Opens in a new window]
BHARAT TALWAR
Affiliation:
Department of Mathematics, University of Delhi, Delhi, India e-mail: btalwar.math@gmail.com
RANJANA JAIN*
Affiliation:
Department of Mathematics, University of Delhi, Delhi, India
*
e-mail: rjain@maths.du.ac.in
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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.

Keywords

vector-valued Beurling algebrasBanach space projective tensor productcentreweightweak amenability

MSC classification

Primary: 46M05: Tensor products
Secondary: 22D15: Group algebras of locally compact groups 43A20: $L^1$-algebras on groups, semigroups, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 3 , June 2022 , pp. 490 - 498
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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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