On some approximate homological properties of certain Banach algebras

We study approximate bi atness and Johnson pseudo-contractibility of Lipschitz algebras. We show that for a compact metric space X; the Lipschitz algebras Lip (X) and ip (X) are approximately bi at if and only if X is nite, provided that 0 < < 1. Also enough and su cient condition for vectorvalued Lipschitz algebras to be Johnson pseudo-contractible is given. We also show that some triangular Banach algebras are not approximately bi at.

Keywords:

Approximate bi atness , Johnson pseudo-contractibility , Lipschitz algebra , triangular Banach algebra.