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Klappentext

Zur Zeit liegt uns keine Inhaltsangabe vor.

Inhalt

I. Some Reminders of Functional Analysis.- II. Some Classes of Operators.- Finite-Dimensional Operators.- Bounded Linear Operators on a Banach Space.- Bounded Linear Operator on a Hilbert Space.- III. Banach Algebras.- Definition and Examples.- Invertible Elements and Spectrum.- Holomorphic Functional Calculus.- Analytic Properties of the Spectrum.- IV. Representation Theory.- Gelfand Theory for Commutative Banach Algebras.- Representation Theory for Non-Commutative Banach Algebras.- V. Some Applications of Subharmonicity.- Some Elementary Applications.- Spectral Characterizations of Commutative Banach Algebras.- Spectral Characterizations of the Radical.- Spectral Characterizations of Finite-Dimensional Banach Algebras.- Automatic Continuity for Banach Algebra Morphisms.- Elements with Finite Spectrum.- Inessential Elements.- VI. Representation of C?-algebras and the Spectral Theorem.- Banach Algebras with Involution.- C?-algebras.- The Spectral Theorem.- Applications.- VII. An Introduction to Analytic Multifunctions.- Definitions and General Properties.- The Oka-Nishino Theorem and Its Applications.- Distribution of Values of Analytic Multifunctions.- Conclusion.- Subharmonic Functions and Capacity.- Functions of Several Complex Variables.- References.- Author and Subject Index.