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Simultaneous Triangularization

  • Heydar Radjavi
  • Peter Rosenthal

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Heydar Radjavi, Peter Rosenthal
    Pages 1-26
  3. Heydar Radjavi, Peter Rosenthal
    Pages 27-42
  4. Heydar Radjavi, Peter Rosenthal
    Pages 43-74
  5. Heydar Radjavi, Peter Rosenthal
    Pages 75-103
  6. Heydar Radjavi, Peter Rosenthal
    Pages 104-129
  7. Heydar Radjavi, Peter Rosenthal
    Pages 130-150
  8. Heydar Radjavi, Peter Rosenthal
    Pages 151-192
  9. Heydar Radjavi, Peter Rosenthal
    Pages 193-243
  10. Heydar Radjavi, Peter Rosenthal
    Pages 244-283
  11. Back Matter
    Pages 284-319

About this book

Introduction

A collection of matrices is said to be triangularizable if there is an invertible matrix S such that S1 AS is upper triangular for every A in the collection. This generalization of commutativity is the subject of many classical theorems due to Engel, Kolchin, Kaplansky, McCoy and others. The concept has been extended to collections of bounded linear operators on Banach spaces: such a collection is defined to be triangularizable if there is a maximal chain of subspaces of the Banach space, each of which is invariant under every member of the collection. Most of the classical results have been generalized to compact operators, and there are also recent theorems in the finite-dimensional case. This book is the first comprehensive treatment of triangularizability in both the finite and infinite-dimensional cases. It contains numerous very recent results and new proofs of many of the classical theorems. It provides a thorough background for research in both the linear-algebraic and operator-theoretic aspects of triangularizability and related areas. More generally, the book will be useful to anyone interested in matrices or operators, as many of the results are linked to other topics such as spectral mapping theorems, properties of spectral radii and traces, and the structure of semigroups and algebras of operators. It is essentially self-contained modulo solid courses in linear algebra (for the first half) and functional analysis (for the second half), and is therefore suitable as a text or reference for a graduate course.

Keywords

algebra Banach Space banach spaces field functional analysis Hilbert space linear algebra matrices matrix maximum operator polynomial semigroup

Authors and affiliations

  • Heydar Radjavi
    • 1
  • Peter Rosenthal
    • 2
  1. 1.Department of MathematicsDalhousie UniversityHalifaxCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1200-3
  • Copyright Information Springer-Verlag New York, Inc. 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98466-7
  • Online ISBN 978-1-4612-1200-3
  • Series Print ISSN 0172-5939
  • Buy this book on publisher's site