A Primer on Spectral Theory [Paperback]

I. Some Reminders of Functional Analysis.- II. Some Classes of Operators.- ?1. Finite-Dimensional Operators.- ?2. Bounded Linear Operators on a Banach Space.- ?3. Bounded Linear Operator on a Hilbert Space.- III. Banach Algebras.- ?1. Definition and Examples.- ?2. Invertible Elements and Spectrum.- ?3. Holomorphic Functional Calculus.- ?4. Analytic Properties of the Spectrum.- IV. Representation Theory.- ?1. Gelfand Theory for Commutative Banach Algebras.- ?2. Representation Theory for Non-Commutative Banach Algebras.- V. Some Applications of Subharmonicity.- ?1. Some Elementary Applications.- ?2. Spectral Characterizations of Commutative Banach Algebras.- ?3. Spectral Characterizations of the Radical.- ?4. Spectral Characterizations of Finite-Dimensional Banach Algebras.- ?5. Automatic Continuity for Banach Algebra Morphisms.- ?6. Elements with Finite Spectrum.- ?7. Inessential Elements.- VI. Representation of C?-algebras and the Spectral Theorem.- ?1. Banach Algebras with Involution.- ?2. C?-algebras.- ?3. The Spectral Theorem.- ?4. Applications.- VII. An Introduction to Analytic Multifunctions.- ?1. Definitions and General Properties.- ?2. The Oka-Nishino Theorem and Its Applications.- ?3. Distribution of Values of Analytic Multifunctions.- ?4. Conclusion.- ?1. Subharmonic Functions and Capacity.- ?2. Functions of Several Complex Variables.- References.- Author and Subject Index.Springer Book Archives