Open Access
2015 Symmetry and inverse closedness for Banach $^*$-algebras associated to discrete groups
Marius Măntoiu
Banach J. Math. Anal. 9(2): 289-310 (2015). DOI: 10.15352/bjma/09-2-19


A discrete group $\mathrm{G}$ is called rigidly symmetric if for every $C^*$-algebra $\mathcal{A}$ the projective tensor product $\ell^1(\mathrm{G})\widehat\otimes A$ is a symmetric Banach $^*$-algebra. For such a group we show that the twisted crossed product $\ell^1_{\alpha,\omega}(\mathrm{G};\mathcal{A})$ is also a symmetric Banach $^*$-algebra, for every twisted action $(\alpha,\omega)$ of $\mathrm{G}$ in a $C^*$-algebra $\mathcal{A}$. We extend this property to other types of decay, replacing the $\ell^1$-condition. We also make the connection with certain classes of twisted kernels, used in a theory of integral operators involving group $2$-cocycles. The algebra of these kernels is studied, both in intrinsic and in represented version.


Download Citation

Marius Măntoiu. "Symmetry and inverse closedness for Banach $^*$-algebras associated to discrete groups." Banach J. Math. Anal. 9 (2) 289 - 310, 2015.


Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1328.47079
MathSciNet: MR3296119
Digital Object Identifier: 10.15352/bjma/09-2-19

Primary: 47L65
Secondary: 22D15 , 43A20 , 47D34

Keywords: crossed product , Discrete group , ‎kernel‎ , symmetric Banach algebra , weight

Rights: Copyright © 2015 Tusi Mathematical Research Group

Vol.9 • No. 2 • 2015
Back to Top