
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 sheaftheoretic 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 StoneWeierstrass theorem. (Author)
Descriptors : *ALGEBRAS, *COMPLEX VARIABLES, ALGEBRAIC TOPOLOGY, FUNCTIONS(MATHEMATICS)
Distribution Statement : APPROVED FOR PUBLIC RELEASE