Illinois Journal of Mathematics

Involutions and trivolutions in algebras related to second duals of group algebras

M. Filali, M. Sangani Monfared, and Ajit Iqbal Singh

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Abstract

We define a trivolution on a complex algebra $A$ as a non-zero conjugate-linear, anti-homomorphism $\tau$ on $A$, which is a generalized inverse of itself, that is, $\tau^{3}=\tau$. We obtain characterizations of trivolutions and show with examples that they appear naturally on many Banach algebras, particularly those arising from group algebras. We give several results on the existence or non-existence of involutions on the dual of a topologically introverted space. We investigate conditions under which the dual of a topologically introverted space admits trivolutions.

Article information

Source
Illinois J. Math., Volume 57, Number 3 (2013), 755-773.

Dates
First available in Project Euclid: 3 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1415023509

Digital Object Identifier
doi:10.1215/ijm/1415023509

Mathematical Reviews number (MathSciNet)
MR3275737

Zentralblatt MATH identifier
1308.46059

Subjects
Primary: 46K05: General theory of topological algebras with involution 22D15: Group algebras of locally compact groups 43A20: $L^1$-algebras on groups, semigroups, etc.

Citation

Filali, M.; Sangani Monfared, M.; Singh, Ajit Iqbal. Involutions and trivolutions in algebras related to second duals of group algebras. Illinois J. Math. 57 (2013), no. 3, 755--773. doi:10.1215/ijm/1415023509. https://projecteuclid.org/euclid.ijm/1415023509


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