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ON ALGEBRA ISOMORPHISMS BETWEEN p-BANACH BEURLING ALGEBRAS

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  11 January 2021

PRAKASH A. DABHI Open the ORCID record for PRAKASH A. DABHI [Opens in a new window]  and
DARSHANA B. LIKHADA Open the ORCID record for DARSHANA B. LIKHADA [Opens in a new window]
PRAKASH A. DABHI
Affiliation:
Department of Mathematics, Institute of Infrastructure Technology Research and Management (IITRAM), Ahmedabad380026, Gujarat, India e-mail: lightatinfinite@gmail.com, prakashdabhi@iitram.ac.in
DARSHANA B. LIKHADA*
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar388120, Gujarat, India Current address: Indian Institute of Teacher Education (IITE), Gandhinagar382016, Gujarat, India e-mail: darshanal@iite.ac.in
*
e-mail: likhada93@gmail.com
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Abstract

Let $(G_1,\omega _1)$ and $(G_2,\omega _2)$ be weighted discrete groups and $0<p\leq 1$ . We characterise biseparating bicontinuous algebra isomorphisms on the p-Banach algebra $\ell ^p(G_1,\omega _1)$ . We also characterise bipositive and isometric algebra isomorphisms between the p-Banach algebras $\ell ^p(G_1,\omega _1)$ and $\ell ^p(G_2,\omega _2)$ and isometric algebra isomorphisms between $\ell ^p(S_1,\omega _1)$ and $\ell ^p(S_2,\omega _2)$ , where $(S_1,\omega _1)$ and $(S_2,\omega _2)$ are weighted discrete semigroups.

Keywords

algebra isomorphismbiseparating and isometric isomorphismsp-Banach algebraweighted Lp algebras for 0 < p ≤ 1

MSC classification

Primary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Secondary: 43A20: $L^1$-algebras on groups, semigroups, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 2 , October 2021 , pp. 308 - 319
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The first author is grateful to SERB, India for the MATRICS grant (MTR/2019/000162). The second author is thankful to UGC-INDIA for National Fellowship for OBC candidates (F./2016-17/NFO-2015-17-OBC-GUJ-46377/SA-III).

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