Bernard Aupetit

A Primer on Spectral Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

Zur Zeit liegt uns keine Inhaltsangabe vor.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 193
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461230489
• Artikelnr.: 44172028

Inhaltsangabe

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.