Ebrahim Samei

Biflatness and Pseudo-Amenability of Segal Algebras

We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L1(G), and the Fourier algebra, A(G), of a locally compact group G. Received by the editors January 9, 2008. Published electronically May 20, 2010. The first author’s research was supported by an NSERC Post Doctoral Fellowship. The second author’s research was supported by NSERC under grant no. 312515-05. The third author’s research was supported by NSERC under grant no. 298444-04. AMS subject classification: 43A20, 43A30, 46H25, 46H10, 46H20, 46L07.

Projectivity of modules over Fourier algebras

In this paper we will study the homological properties of various natural modules associated to the Fourier algebra of a locally compact group. In particular, we will focus on the question of identifying when such modules will be projective in the category of operator spaces. We will show that pro- jectivity often implies that the underlying group is discrete and give evidence to show that amenability also plays an important role. Over the past thirty years there has been a rich body of work dedicated to understanding the cohomological properties of the various Banach algebras arising in the study of locally compact groups. The seminal paper in this respect is certainly Barry Johnsons memoir (22) in which he introduces the concept of amenability for a Banach algebra, and shows that for a locally compact group G the group algebra L 1 (G) is amenable if and only if G is amenable in the classical sense. While applications of cohomology to harmonic anlysis may be more celebrated, there have also been a number of significant studies related to the homological properties of the algebras arising from groups. Recently, H. G. Dales and M. E. Polyakov (12) gave a detailed study of the homological properties of modules over the group algebra of a locally compact group. In their work they focused primarily on the question of whether or not certain natural left L 1 (G)-modules are respectively projective, injective, or flat. They were able to show, for example, that when viewed as the dual left-module of L 1 (G), L ∞ (G) is projective precisely when the group G is finite. In stark contrast, they prove that L ∞ (G) is always injective. They also showed that the measure algebra M(G) is projective precisely when G is discrete, while in this case injectivity is equivalent to the group G being amenable. When G is abelian the classical Fourier transform identifies L 1 (G) with a com-

Bounded and completely bounded local derivations from certain commutative semisimple Banach algebras

We show that for a locally compact group G, every completely bounded local derivation from the Fourier algebra A(G) into a symmetric operator A(G)-module or the operator dual of an essential A(G)-bimodule is a derivation. Moreover, for amenable G we show that the result is true for all operator A(G)-bimodules. In particular, we derive a new proof to a result of N. Spronk that A(G) is always operator weakly amenable.

The moment problem for continuous positive semidefinite linear functionals

Let τ be a locally convex topology on the countable dimensional polynomial

Reflexivity and hyperreflexivity of bounded

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-cocycles from group algebras

-algebra

Weak amenability and 2-weak amenability of Beurling algebras

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