Several complex variables and Banach algebras /

• Main Author: Alexander, Herbert
• Other Authors: Wermer, John
• Format: eBook
• Language: English
• Published: New York : Springer, �1998.
• Edition: 3rd ed.
• Series: Graduate texts in mathematics ; 35.
• Subjects: Banach algebras.; Functions of several complex variables.; Banach, Alg�ebres de.; Fonctions de plusieurs variables complexes.; MATHEMATICS > Algebra > Linear.; Electronic books.

Many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. While function theory has often been employed to answer algebraic questions such as the existence of idempotents in a Banach algebra, concepts aris...

Table of Contents:

• Preliminaries and Notations
• Classical Approximation Theorems
• Operational Calculus in One Variable
• Differential Forms
• The *-Operator
• The Equation
• The Oka-Weil Theorem
• Operational Calculus in Several Variables
• The Silov Boundary
• Maximality and Rado's Theorem
• Maximum Modulus Algebras
• Hulls of Curves and Arcs
• Integral Kernels
• Perturbations of the Stone-Weierstrass Theorem
• The First Cohomology Group of a Maximal Ideal Space
• The *-Operator in Smoothly Bounded Domains
• Manifolds with Complex Tangents
• Submanifolds of High Dimension
• Boundaries of Analytic Varieties
• Polynomial Hulls of Sets over the Circle
• Areas
• Topology of Hulls
• Pseudoconvex Sets in Cn
• Examples
• Historical Comments and Recent Developments
• Appendix
• Solutions of Some Exercises. Bibliography. Additional Bibliography. Index.