Title of article :
On I-biflat and I-biprojective Banach algebras
Author/Authors :
Sahami ، Amir Department of Mathematics - Faculty of Basic Science - Ilam University , Rostami ، Mehdi Faculty of Mathematics and Computer Science - Amirkabir University of Technology , Kalantari ، Shahab Department of Basic Sciences - Babol Noshirvani University of Technology
Abstract :
In this paper, we introduce new notions of $I$-biflatness and $I$-biprojectivity, for a Banach algebra $A$, where $I$ is a closed ideal of $A$. We show that $M(G)$ is $L^{1}(G)$-biprojective ($I$-biflat) if and only if $G$ is a compact group (an amenable group), respectively. Also, we show that, for a non-zero ideal $I$, if the Fourier algebra $A(G)$ is $I$-biprojective, then $G$ is a discrete group. Some examples are given to show the differences between these new notions and the classical ones.
Keywords :
I , biflatness , I , biprojectivity , Banach algebra
Journal title :
Wavelets and Linear Algebra
Journal title :
Wavelets and Linear Algebra
