Search

In this paper, we introduce a notion of Connes biprojectivity for a dual Banach algebra A with respect to its w∗-closed ideal I, say I-Connes biprojectivity. Some Lipschitz algebras Lipα(X) and some matrix algebras are studied under this new notion. Also, with some mild assumptions, the relation between IConnes biprojectivity and left ϕ-contractibility is given, where ϕ is a ω∗-continuous multiplicative linear functional on A. As an application, we characterize Connes biprojectivity of some Lipschitz algebras. [ABSTRACT FROM AUTHOR]

We continue [8] and we discuss approximately left ϕ-biprojectivity for θ-Lau product algebras. We give some Banach algebras among the category of θ-Lau product algebras which are not approximately left ϕ-biprojective. In fact, some class of matrix algebras under the notion of approximate left ϕ-biprojectivity is also discussed here. [ABSTRACT FROM AUTHOR]