Analysis seminar

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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