# 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

Involutions and trivolutions on second dual of algebras related to locally compact groups and topological semigroups

- Mathematics
- 2017

We investigate involutions and trivolutions in the second dual of algebras related to a locally compact topological semigroup and the Fourier algebra of a locally compact group. We prove, among the… Expand

Involutions on the second duals of group algebras versus subamenable groups

- Mathematics
- 2011

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 is… Expand

#### References

SHOWING 1-10 OF 38 REFERENCES

INVOLUTIONS ON THE SECOND DUALS OF GROUP ALGEBRAS AND A MULTIPLIER PROBLEM

- Mathematics
- Proceedings of the Edinburgh Mathematical Society
- 2007

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 the… Expand

Algebra involutions on the bidual of a Banach algebra

- Mathematics
- 1984

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) is… Expand

The Second Duals of Beurling Algebras

- Mathematics
- 2005

Introduction Definitions and preliminary results Repeated limit conditions Examples Introverted subspaces Banach algebras of operators Beurling algebras The second dual of $\ell^1(G,\omega)$ Algebras… Expand

MODULE HOMOMORPHISMS AND TOPOLOGICAL CENTRES ASSOCIATED WITH WEAKLY SEQUENTIALLY COMPLETE BANACH ALGEBRAS

- Mathematics
- 1998

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 in… Expand

Endomorphisms of symbolic algebraic varieties

- Mathematics
- 1999

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 paper… Expand

The norm-strict bidual of a Banach algebra and the dual of Cu(G)

- Mathematics
- 1984

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

- Mathematics
- 2010

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) the… Expand

Involutions on the second duals of group algebras versus subamenable groups

- Mathematics
- 2011

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 is… Expand

One-sided ideals and right cancellation in the second dual of the group algebra and similar algebras

- Mathematics
- 2007

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

- Mathematics
- 1996

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