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Abstract: In this paper we will study the projetivity of various natural modulesassociated to operator Segal algebras of the Fourier algebra of a locallycompact group. In particular, we will focus on the question of identifying whensuch modules will be projective in the category of operator spaces.Projectivity often implies that the underlying group is discrete or evenfinite. We will also look at the projectivity for modules of $A {cb}G$, theclosure of $AG$ in the space of its completely bounded mutipliers. Here wegive an evidence to show that weak amenability of $G$ plays an important role.



Author: Brian E. Forrest, Hun Hee Lee, Ebrahim Samei

Source: https://arxiv.org/



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