A primer on spectral theory

著者

• Aupetit, Bernard

書誌事項

A primer on spectral theory

Bernard Aupetit

（Universitext）

Spring-Verlag, c1991

• : us
• : gw

注記

Includes bibliographical references and index

内容説明・目次

巻冊次

: us ISBN 9780387973906

目次

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.

巻冊次

: gw ISBN 9783540973904

内容説明

This textbook provides an introduction to the new techniques of subharmonic functions and analytic multifunctions in spectral theory. Topics include the basic results of functional analysis, bounded operations on Banach algebras, and applications of spectral subharmonicity. Each chapter is followed by exercises of varying difficulty. Much of the subject matter, particularly in spectral theory, operator theory and Banach algebras, contains new results.

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詳細情報

• NII書誌ID(NCID): BA11532763
• ISBN:
  • 0387973907
  • 3540973907
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: New York
• ページ数/冊数: xii, 193 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA320
  • DC20 : 515/.7222
  • NDC8 : 415.52
• 件名:
  • LCSH : Spectral theory (Mathematics)
• 親書誌ID:
  • BA00021004