Character contractibility of Banach algebras and homological properties of Banach modules

Volume 202 / 2011

Rasoul Nasr-Isfahani, Sima Soltani Renani Studia Mathematica 202 (2011), 205-225 MSC: Primary 46H25, 43A07; Secondary 22D15, 46H05. DOI: 10.4064/sm202-3-1

Abstract

Let ${\cal A}$ be a Banach algebra and let $\phi$ be a nonzero character on ${{\cal A}}$. We give some necessary and sufficient conditions for the left $\phi$-contractibility of ${\cal A}$ as well as several hereditary properties. We also study relations between homological properties of some Banach left ${\cal A}$-modules, the left $\phi$-contractibility and the right $\phi$-amenability of ${\cal A}$. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.

Authors

  • Rasoul Nasr-IsfahaniDepartment of Mathematical Sciences
    Isfahan University of Technology
    Isfahan 84156-83111, Iran
    e-mail
  • Sima Soltani RenaniDepartment of Mathematical Sciences
    Isfahan University of Technology
    Isfahan 84156-83111, Iran
    e-mail

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