Details

Autor(en) / Beteiligte

• Müller, Vladimir

Titel

Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras [electronic resource]

Auflage

1st ed. 2003

Ort / Verlag

Basel : Birkhäuser Basel

Erscheinungsjahr

2003

Link zum Volltext

• SpringerLink Books - AutoHoldings

Beschreibungen/Notizen

• Bibliographic Level Mode of Issuance: Monograph
• I Banach Algebras -- II Operators -- III Essential Spectrum -- IV Taylor Spectrum -- V Orbits and Capacity -- A.l Banach spaces -- A.2 Analytic vector-valued functions -- A.3 C°-functions -- A.4 Semicontinuous set-valued functions -- List of Symbols.
• This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. Due to its very clear style and the careful organization of the material, this truly brilliant book may serve as an introduction into the field, yet it also provides an excellent source of information on specific topics in spectral theory for the working mathematician. Review of the first edition by M. Grosser, Vienna Monatshefte für Mathematik Vol. 146, No. 1/2005.
• English
• Description based on publisher supplied metadata and other sources.