Segal algebras, approximate identities and norm irregularity in $C_0(X,A)$
Volume 215 / 2013
Studia Mathematica 215 (2013), 99-112
MSC: Primary 46J10; Secondary 46H05.
DOI: 10.4064/sm215-2-1
Abstract
We study three closely related concepts in the context of the Banach algebra $C_0(X,A)$. We show that, to a certain extent, Segal extensions, norm irregularity and the existence of approximate identities in $C_0(X,A)$ can be deduced from the corresponding features of $A$ and vice versa. Extensive use is made of the multiplier norm and the tensor product representation of $C_0(X,A)$.
