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BIPROJECTIVITY AND BIFLATNESS OF LAU PRODUCT OF BANACH ALGEBRAS DEFINED BY A BANACH ALGEBRA MORPHISM
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 1 / February 2015
- Published online by Cambridge University Press:
- 15 July 2014, pp. 134-144
- Print publication:
- February 2015
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- Article
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- You have access
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Let
${\it\varphi}$ be a homomorphism from a Banach algebra 
${\mathcal{B}}$ to a Banach algebra 
${\mathcal{A}}$. We define a multiplication on the Cartesian product space 
${\mathcal{A}}\times {\mathcal{B}}$ and obtain a new Banach algebra 
${\mathcal{A}}\times _{{\it\varphi}}{\mathcal{B}}$. We show that biprojectivity as well as biflatness of 
${\mathcal{A}}\times _{{\it\varphi}}{\mathcal{B}}$ are stable with respect to 
${\it\varphi}$.
