I. Some Reminders of Functional Analysis -- II. Some Classes of Operators -- ยง1. Finite-Dimensional Operators -- ยง2. Bounded Linear Operators on a Banach Space -- ยง3. Bounded Linear Operator on a Hilbert Space -- III. Banach Algebras -- ยง1. Definition and Examples -- ยง2. Invertible Elements and Spectrum -- ยง3. Holomorphic Functional Calculus -- ยง4. Analytic Properties of the Spectrum -- IV. Representation Theory -- ยง1. Gelfand Theory for Commutative Banach Algebras -- ยง2. Representation Theory for Non-Commutative Banach Algebras -- V. Some Applications of Subharmonicity -- ยง1. Some Elementary Applications -- ยง2. Spectral Characterizations of Commutative Banach Algebras -- ยง3. Spectral Characterizations of the Radical -- ยง4. Spectral Characterizations of Finite-Dimensional Banach Algebras -- ยง5. Automatic Continuity for Banach Algebra Morphisms -- ยง6. Elements with Finite Spectrum -- ยง7. Inessential Elements -- VI. Representation of C?-algebras and the Spectral Theorem -- ยง1. Banach Algebras with Involution -- ยง2. C?-algebras -- ยง3. The Spectral Theorem -- ยง4. Applications -- VII. An Introduction to Analytic Multifunctions -- ยง1. Definitions and General Properties -- ยง2. The Oka-Nishino Theorem and Its Applications -- ยง3. Distribution of Values of Analytic Multifunctions -- ยง4. Conclusion -- ยง1. Subharmonic Functions and Capacity -- ยง2. Functions of Several Complex Variables -- References -- Author and Subject Index

1. Mathematics
2. Topological groups
3. Lie groups
4. Mathematical analysis
5. Analysis (Mathematics)
6. Mathematics
7. Analysis
8. Topological Groups
9. Lie Groups