2 research outputs found
Regularity conditions for vector-valued function algebras
We consider several notions of regularity, including strong regularity,
bounded relative units, and Ditkin's condition, in the setting of vector-valued
function algebras. Given a commutative Banach algebra and a compact space
, let be a Banach -valued function algebra on and let
be the subalgebra of consisting of scalar-valued
functions. This paper is about the connection between regularity conditions of
the algebra and the associated algebras and .
That inherits a certain regularity condition to
and is the easy part of the problem. We investigate the
converse and show that, under certain conditions, receives
form and . The results apply to tensor products of
commutative Banach algebras as they are included in the class of vector-valued
function algebras