Sebastien Guex, University of Alberta
“Ergodic theorems for certain Banach algebras associated to locally compact groups.”
Since 1964 and the pioneering work of P. Eymard, the Fourier algebra of a locally compact group has been studied under many aspects, and provide a natural framework for the extension of many classical results in commutative harmonic analysis to the non-commutative case. Later on, A. Figa-Talamanca and C. S. Herz considered an Lp- analogue of the Fourier algebra, which is nowadays known as the Figa-Talamanca-Herz algebra. In this talk, we shall discuss some ergodic results related to these algebras. In particular, after characterizing their non- degenerate ∗-representations, we shall study ergodic sequences and ergodic multipliers. Finally, we shall also present a mean ergodic theorem for a larger class of Banach algebras, which include the aforementioned ones.
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