Some banach algebras of analytic functions

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Linda Louise Stanfield (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Hughes Hoyle

Abstract: The purpose of the paper is to investigate the ideal structure in two Banach Algebras: A, the space of all complex-valued functions which are continuous on the closed unit disc U in the complex plane and analytic on the open unit disc U, and Hoo , the space of all bounded analytic functions on U. Some basic concepts of Banach Algebras are developed; the existence of a one-to-one correspondence between the set of all maximal ideals of a Banach Algebra X and the set M/(X) of all homomorphisms from X to C is shown; a topology with respect to which A/(X) is a compact Hausdorff space is exhibited. The investigation of the ideal structure in A and Hoo shows that every maximal ideal in A is the kernel of an evaluation on A; M(A) is horaeomorphic to U; each z ? U with |z| =1 corresponds to infinitely many ideals in W(Hoo ). Finally, it is shown that the Silov boundary of Hoo is a proper subset of those ideals in W(Hoo ) which correspond to points z ? U where |z| = 1.

Additional Information

Language: English
Date: 1970
Banach algebras
Analytic functions

Email this document to