Accession Number : AD0268887

Title :   APPLICATIONS OF SHEAF THEORY TO FUNCTION ALGEBRAS

Corporate Author : STANFORD UNIV CALIF APPLIED MATHEMATICS AND STATISTICS LABS

Personal Author(s) : HURD,ALBERT E.

Report Date : 27 SEP 1961

Pagination or Media Count : 1

Abstract : A representation theory is developed for an arbitrary commutative algebra with identity in terms of al algebra of continuous functions on a suitable topological space. A brief survey is presented of the theory of coherent analytic sheaves. No attempt at completeness is made; the object being to collect in one place the definitions and results. The sheaf-theoretic results are then used to investigate algebras of holomorphic functions on the special class of complex manifolds, the Stein manifolds. A simple example is presented to point out the error of a theorem stating that the functions on the maximal ideal space of a Banach algebra, which came from elements of the algebra via the Gelfand respresentation, enjoy a certain local characterization, much as do analytic functions on a complex manifold, or continuous functions on a topological space. The appendix contains a proof of the generalization of the Stone-Weierstrass theorem. (Author)

Descriptors :   *ALGEBRAS, *COMPLEX VARIABLES, ALGEBRAIC TOPOLOGY, FUNCTIONS(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE