ABSTRACT

This book presents a detailed account of some results about subalgebras of C(X), which carry a Banach algebra norm. It is intended for students who have had a standard graduate real-variable course and be acquainted with a few odds and ends of functional analysis and complex-variables.

chapter |4 pages

Some Notations and General Remarks

chapter Chapter I|11 pages

Bishop’s Stone-Weierstrass Theorem

chapter Chapter II|13 pages

Restriction Algebras Determining C(X)

chapter Chapter IV|28 pages

The Work of Alain Bernard

chapter Chapter V|20 pages

The Theorems of Gorin and Čirka

chapter Chapter VII|15 pages

Katznelson’s Bounded Idempotent Theorem

chapter Chapter VIII|9 pages

Characterization of C(X) by Functions which Operate