Open Access
november 2013 On $\phi$-biflat and $\phi$-biprojective Banach algebras
A. Sahami, A. Pourabbas
Bull. Belg. Math. Soc. Simon Stevin 20(5): 789-801 (november 2013). DOI: 10.36045/bbms/1385390764


In this paper, we introduce the new notions of $\phi$-biflatness, $\phi$-biprojectivity, $\phi$-Johnson amenability and $\phi$-Johnson contractibility for Banach algebras, where $\phi$ is a non-zero homomorphism from a Banach algebra $A$ into $\mathbb{C}$. We show that a Banach algebra $A$ is $\phi$-Johnson amenable if and only if it is $\phi$-inner amenable and $\phi$-biflat. Also we show that $\phi$-Johnson amenability is equivalent with the existence of left and right $\phi$-means for $A$. We give some examples to show differences between these new notions and the classical ones. Finally, we show that ${L^{1}(G)}$ is $\phi$-biflat if and only if $G$ is an amenable group and $A(G)$ is $\phi$-biprojective if and only if $G$ is a discrete group.


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A. Sahami. A. Pourabbas. "On $\phi$-biflat and $\phi$-biprojective Banach algebras." Bull. Belg. Math. Soc. Simon Stevin 20 (5) 789 - 801, november 2013.


Published: november 2013
First available in Project Euclid: 25 November 2013

zbMATH: 1282.43001
MathSciNet: MR3160589
Digital Object Identifier: 10.36045/bbms/1385390764

Primary: ‎43A07‎ , 43A20
Secondary: 46H05

Keywords: $\phi$-amenability , $\phi$-biflatness , $\phi$-biprojectivity , $\phi$-inner amenability , Banach Algebra

Rights: Copyright © 2013 The Belgian Mathematical Society

Vol.20 • No. 5 • november 2013
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