Document Type

Presentation Abstract

Presentation Date

4-15-2013

Abstract

Let X be a completely regular Hausdorff space and A be a complex commutative unital Banach algebra with norm ∥∥∞. We denote by C (X, A) the unital algebra of all A-valued continuous functions on X with pointwise operations and unit element e (x)≡e, where e is the unit element of A. We denote by (Cb (X, A), ∥∥∞) the subalgebra of C (X, A) of all bounded continuous functions, provided with the sup-norm ∥∥∞ on X given by

[Download the attached PDF file to see the equation here and the complete abstract.]

for every ƒ ∈Cb(X, A), and by (Cp(X, A), ∥∥∞) the subalgebra of all functions ƒ ∈Cb(X, A) such that ̅ƒ ̅(̅X̅) is compact in A. It is easy to see that both are Banach algebras.

We study the maximal ideal space M ((Cb(X, A), ∥∥∞)), invertibility in (Cb(X, A), ∥∥∞) and establish necessary and sufficient conditions in order the set X × M (A) to be dense in M((Cb(X, A), ∥∥∞)) where M(A) is the maximal ideal space of A.

Additional Details

Presented jointly with the Analysis Seminar.

Monday, 15 April 2013
3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109

Download

Share

COinS