A Primer on Spectral Theory

Inhaltsverzeichnis

• 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.