Character amenability of Banach algebras

By M. S. Monfared. Mathematical Proceedings of the Cambridge Philosophical Society, 2008

158 citations recorded by the source corpus.

Abstract We introduce the notion of character amenable Banach algebras. We prove that character amenability for either of the group algebra L1(G) or the Fourier algebra A(G) is equivalent to the amenability of the underlying group G. Character amenability of the measure algebra M(G) is shown to be equivalent to G being a discrete amenable group. We also study functorial properties of character amenability. For a commutative character amenable Banach algebra A, we prove all cohomological groups with coefficients in finite-dimensional Banach A-bimodules, vanish. As a corollary we conclude that all finite-dimensional extensions of commutative character amenable Banach algebras split strongly.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d102628bbcdf7329b497023eca07384220c87e51

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In Algebra and Number Theory

1. Rasoul Nasr-Isfahani
2. M. Nemati
3. M. Alaghmandan
4. M. S. Monfared
5. A. Alinejad
6. A. Ghaffari

In Mathematical Physics

1. Rasoul Nasr-Isfahani
2. M. Nemati
3. M. Alaghmandan
4. M. S. Monfared
5. Tim Traynor
6. Zhiguo Hu
7. A. Alinejad
8. A. Ghaffari

Citations in the corpus

• On character amenable Banach algebras (2009, background): “Runde [30], and more recently character amenability by Kaniuth-Lau-Pym [25] and Sangani Monfared [31].”
• CHARACTER AMENABILITY AND CONTRACTIBILITY OF ABSTRACT SEGAL ALGEBRAS (2010, background): “[7, 8] introduced and studied the concept of φ-amenability for Banach algebras as a generalization of left amenability of Lau algebras.”