Invertibility and Singularity for Bounded Linear Operators (eBook)

Robin Harte (Autor)

eBook Download: EPUB

2016
624 Seiten
Dover Publications (Verlag)
978-0-486-81788-0 (ISBN)

Infos

Suitable for courses in functional analysis and a valuble resource for researchers, this introductory treatment is based on the open mapping theorem, Hahn-Banach theorem, dual space construction, enlargement of normed space, and Liouville's theorem. 1988 edition.

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This introduction to functional analysis focuses on the types of singularity that prevent an operator from being invertible. The presentation is based on the open mapping theorem, Hahn-Banach theorem, dual space construction, enlargement of normed space, and Liouville's theorem. Suitable for advanced undergraduate and graduate courses in functional analysis, this volume is also a valuable resource for researchers in Fredholm theory, Banach algebras, and multiparameter spectral theory. The treatment develops the theory of open and almost open operators between incomplete spaces. It builds the enlargement of a normed space and of a bounded operator and sets up an elementary algebraic framework for Fredholm theory. The approach extends from the definition of a normed space to the fringe of modern multiparameter spectral theory and concludes with a discussion of the varieties of joint spectrum. This edition contains a brief new Prologue by author Robin Harte as well as his lengthy new Epilogue, "e;Residual Quotients and the Taylor Spectrum."e; Dover republication of the edition published by Marcel Dekker, Inc., New York, 1988.

Autor

Robin Harte received his PhD from the University of Cambridge and taught at the University Colleges of Swansea and Cork in addition to visiting the universities of Iowa, Fairbanks, Lille, and Mexico. He remains loosely affiliated with Trinity College, Dublin, and is the author of Spectral Mapping Theorems: A Bluffer's Guide.

Inhalt

ProloguePreface1. Normed Linear Spaces2. Bounded Linear Operators3. Invertibility and Singularity4. Banach Spaces and Completeness5. Linear Functions and Duality6. Finite Dimensional Spaces and Compactness7. Operator Algebra nand Commutivity8. Inner Products and Orthogonality9. Liouville's Theorem and Spectral Theory10. Comparisons of Operators and Exactness11. Multiparameter Spectral Theory EpilogueNotes, Comments, and ExercisesReferencesNotationIndex

Produkt-Details

• Erscheint lt. Verlag: 16.11.2016
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 150 x 150 mm
• Gewicht: 880 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: Algebra • arieties of joint spectrum • books about math • bounded linear operators • Calculus • Complex • Dual Space construction • enlargement of normed space • Finite Dimensional Spaces • Functional Analysis • Geometry • Hahn-Banach theorem • Liouville's Theorem • mathematical studies • Mathematics • modern multiparameter spectral theory • Non-fiction • Normed linear spaces • normed space • Open mapping theorem • Operator algebra • Operators in Mathematics • science and math, Functional analysis • spectral theory • Taylor Spectrum
• ISBN-10: 0-486-81788-1 / 0486817881
• ISBN-13: 978-0-486-81788-0 / 9780486817880