Involutions and Trivolutions in Algebras Related to Second Duals of Group Algebras

@article{Filali2012InvolutionsAT,
  title={Involutions and Trivolutions in Algebras Related to Second Duals of Group Algebras},
  author={Mahmoud Filali and Mehdi Sangani Monfared and Ajit Iqbal Singh},
  journal={arXiv: Functional Analysis},
  year={2012}
}
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 give several 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… Expand
2 Citations
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References

SHOWING 1-10 OF 38 REFERENCES
INVOLUTIONS ON THE SECOND DUALS OF GROUP ALGEBRAS AND A MULTIPLIER PROBLEM
Abstract We show that if a locally compact group $G$ is non-discrete or has an infinite amenable subgroup, then the second dual algebra $L^1(G)^{**}$ does not admit an involution extending theExpand
Algebra involutions on the bidual of a Banach algebra
Let A be a Banach algebra with bounded approximate right identity. We show that a necessary condition for the bidual of A to admit an algebra involution (with respect to the first Arens product) isExpand
The Second Duals of Beurling Algebras
Introduction Definitions and preliminary results Repeated limit conditions Examples Introverted subspaces Banach algebras of operators Beurling algebras The second dual of $\ell^1(G,\omega)$ AlgebrasExpand
MODULE HOMOMORPHISMS AND TOPOLOGICAL CENTRES ASSOCIATED WITH WEAKLY SEQUENTIALLY COMPLETE BANACH ALGEBRAS
Abstract This paper is a contribution to the theory of weakly sequentially complete Banach algebras A . We require them to have bounded approximate identities and, for the most part, to be ideals inExpand
Endomorphisms of symbolic algebraic varieties
The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paperExpand
The norm-strict bidual of a Banach algebra and the dual of Cu(G)
To each Banach algebra A we associate a (generally) larger Banach algebra A+ which is a quotient of its bidual A″. It can be constructed using the strict topology on A and the Arens product on A″. A+Expand
On ideals in the bidual of the Fourier algebra and related algebras
Let G be a compact nonmetrizable topological group whose local weight b(G) has uncountable cofinality. Let H be an amenable locally compact group, A(G×H) the Fourier algebra of G×H, and UC2(G×H) theExpand
Involutions on the second duals of group algebras versus subamenable groups
Let L1(G)∗∗ be the second dual of the group algebra L(G) of a locally compact group G. We study the question of involutions on L1(G)∗∗. A new class of subamenable groups is introduced which isExpand
One-sided ideals and right cancellation in the second dual of the group algebra and similar algebras
The following results are proved for a non-compact, locally compact group G: the dimension of every non-trivial right ideal in L1(G)** (equipped with the first Arens product) is at least , where (G)Expand
On the set of topologically invariant means on an algebra of convolution operators on
Let G be a locally compact group, Ap = Ap(G) the Banach algebra defined by Herz; thus A2(G) = A(G) is the Fourier algebra of G. Let PMp = A* the dual, J C Ap a closed ideal, with zero set F = Z(J),Expand
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