Let ϕ be a homomorphism from a Banach algebra B to a Banach algebra A. We define a multiplication on the Cartesian product space A × B and obtain a new Banach algebra A × ϕ B. We show that biprojectivity as well as biflatness of A × ϕ B are stable with respect to ϕ.2010 Mathematics subject classification: primary 46M10; secondary 46H25, 46M18.
Let T be a Banach algebra homomorphism from a Banach algebra B to a Banach algebra A with T ≤ 1. Recently, Bhatt and Dabhi ['Arens regularity and amenability of Lau product of Banach algebras defined by a Banach algebra morphism', Bull. Aust. Math. Soc. 87 (2013), 195-206] showed that cyclic amenability of A × T B is stable with respect to T , for the case where A is commutative. In this note, we address a gap in the proof of this stability result and extend it to an arbitrary Banach algebra A.2010 Mathematics subject classification: primary 46H05; secondary 46H99.
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