ROOM ONE: Orlicz algebras on locally compact groups
Let G be a locally compact group, Φ be a Young function, and denote
by LΦ(G) the associated Orlicz space.
This talk is a survey of results on Banach algebra and Banach module
structures of Orlicz spaces on G that we have obtained recently in
collaboration with our colleagues.
We present conditions for an Orlicz algebra to be Arens regular.
We investigate their cohomological properties such as amenability.
We determine when an Orlicz algebra is an operator algebra.
Our approach can be applied to a vast variety of cases and extend the
results in the classical situation.
This presentation is based on joint works with Ebrahim Samei and
Varvara Shepelska of University of Saskatchewan, Canada.