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22nd Conference in Operator Theory
July 3-8, 2008
West University
Timisoara, Romania |
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Institute of Mathematics of the Romanian Academy and West University in Timisoara
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The modulus of right multipliers on group algebras
by
Ali Ghaffari
Department of Mathematics, Semnan University, Semnan, IRAN
Abstract
Let G be a locally compact group. In the talk we shall discuss
the modulus of right multipliers on second dual of group algebras
and modulus of operators on L∞(G) which commute with
convolutions.
The main results of our investigations are the
following theorems:
Theorem 1 The following statements
hold:
(1) For m ∈ M(G), |rm*|=r|m|*
where rm is right multiplier on M(G).
(2) If
n ∈ LUC(G)⊥ and n ≠ 0, then |Tn| ≠ T|n| where
Tn(m)=nm.
Theorem 2 Let G be a compact group
and m ∈ L1(G). Then |rm|=r|m|.
Theorem 3 For m ∈ L1(G),
|rm**|=r|m|** whenever one of the
following conditions
holds:
(1) G is a compact group.
(2)
|rm**| is compact.
(3) |rm**| is
weak*-weak* continuous.
Date received: March 24, 2008
Copyright © 2008 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # cawh-13.