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Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We introduce and study a new notion of amenability for 𝓐 based on existence of a ϕ-approximate diagonal by modifying the concepts of ϕ-amenability and pseudo-amenability. We then apply these results to characterize ϕ-pseudo-amenability of various Banach algebras related to locally compact groups such as group algebras, measure algebras, certain dual algebras and Lebesgue-Fourier algebras.
Rasoul Nasr-Isfahani, and Mehdi Nemati. "Character pseudo-amenability of Banach algebras." Colloquium Mathematicae 132.2 (2013): 177-193. <http://eudml.org/doc/284305>.
@article{RasoulNasr2013, abstract = {Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We introduce and study a new notion of amenability for 𝓐 based on existence of a ϕ-approximate diagonal by modifying the concepts of ϕ-amenability and pseudo-amenability. We then apply these results to characterize ϕ-pseudo-amenability of various Banach algebras related to locally compact groups such as group algebras, measure algebras, certain dual algebras and Lebesgue-Fourier algebras.}, author = {Rasoul Nasr-Isfahani, Mehdi Nemati}, journal = {Colloquium Mathematicae}, keywords = {Banach algebra; character pseudo-amenability; group algebra; mean; locally compact group; Lebesgue-Fourier algebra}, language = {eng}, number = {2}, pages = {177-193}, title = {Character pseudo-amenability of Banach algebras}, url = {http://eudml.org/doc/284305}, volume = {132}, year = {2013}, }
TY - JOUR AU - Rasoul Nasr-Isfahani AU - Mehdi Nemati TI - Character pseudo-amenability of Banach algebras JO - Colloquium Mathematicae PY - 2013 VL - 132 IS - 2 SP - 177 EP - 193 AB - Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We introduce and study a new notion of amenability for 𝓐 based on existence of a ϕ-approximate diagonal by modifying the concepts of ϕ-amenability and pseudo-amenability. We then apply these results to characterize ϕ-pseudo-amenability of various Banach algebras related to locally compact groups such as group algebras, measure algebras, certain dual algebras and Lebesgue-Fourier algebras. LA - eng KW - Banach algebra; character pseudo-amenability; group algebra; mean; locally compact group; Lebesgue-Fourier algebra UR - http://eudml.org/doc/284305 ER -