Bibliographic Information

Simultaneous triangularization

Heydar Radjavi, Peter Rosenthal

(Universitext)

Springer, c2000

  • : hbk
  • : pbk

Available at  / 35 libraries

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Note

Includes bibliographical references (p. [284]-305) and indexes

Description and Table of Contents

Description

This volume is designed to appeal to two different, yet intersecting audiences: linear algebraists and operator theorists. The first half contains a thorough treatment of classical and recent results on triangularization of collections of matrices, while the remainder describes what is known about extensions to linear operators on Banach spaces. It will thus be useful to everyone interested in matrices or operators since the results involve many other topics.

Table of Contents

One: Algebras of Matrices.- 1.1 The Triangularization Lemma.- 1.2 Burnside's Theorem.- 1.3 Triangularizability of Algebras of Matrices.- 1.4 Triangularization and the Radical.- 1.5 Block Triangularization and Characterizations of Triangularizability.- 1.6 Approximate Commutativity.- 1.7 Nonassociative Algebras.- 1.8 Notes and Remarks.- Two: Semigroups of Matrices.- 2.1 Basic Definitions and Propositions.- 2.2 Permutable Trace.- 2.3 Zero-One Spectra.- 2.4 Notes and Remarks.- Three: Spectral Conditions on Semigroups.- 3.1 Reduction to the Field of Complex Numbers.- 3.2 Permutable Spectrum.- 3.3 Submultiplicative Spectrum.- 3.4 Conditions on Spectral Radius.- 3.5 The Dominance Condition on Spectra.- 3.6 Notes and Remarks.- Four: Finiteness Lemmas and Further Spectral Conditions.- 4.1 Reductions to Finite Semigroups.- 4.2 Subadditive and Sublinear Spectra.- 4.3 Further Multiplicative Conditions on Spectra.- 4.4 Polynomial Conditions on Spectra.- 4.5 Notes and Remarks.- Five: Semigroups of Nonnegative Matrices.- 5.1 Decomposability.- 5.2 Indecomposable Semigroups.- 5.3 Connections with Reducibility.- 5.4 Notes and Remarks.- Six: Compact Operators and Invariant Subspaces.- 6.1 Operators on Banach Spaces.- 6.2 Compact Operators.- 6.3 Invariant Subspaces for Compact Operators.- 6.4 The Riesz Decomposition of Compact Operators.- 6.5 Trace-Class Operators on Hilbert Space.- 6.6 Notes and Remarks.- Seven: Algebras of Compact Operators.- 7.1 The Definition of Triangularizability.- 7.2 Spectra from Triangular Forms.- 7.3 Lomonosov's Lemma and McCoy's Theorem.- 7.4 Transitive Algebras.- 7.5 Block Triangularization and Applications.- 7.6 Approximate Commutativity.- 7.7 Notes and Remarks.- Eight: Semigroups of Compact Operators.- 8.1 Quasinilpotent Compact Operators.- 8.2 A General Approach.- 8.3 Permutability and Submultiplicativity of Spectra.- 8.4 Subadditivity and Sublinearity of Spectra.- 8.5 Polynomial Conditions on Spectra.- 8.6 Conditions on Spectral Radius and Trace.- 8.7 Nonnegative Operators.- 8.8 Notes and Remarks.- Nine: Bounded Operators.- 9.1 Collections of Nilpotent Operators.- 9.2 Commutators of Rank One.- 9.3 Bands.- 9.4 Nonnegative Operators.- 9.5 Notes and Remarks.- References.- Notation Index.- Author Index.

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Details

  • NCID
    BA45531524
  • ISBN
    • 0387984674
    • 0387984666
  • LCCN
    99023772
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    New York ; Tokyo
  • Pages/Volumes
    xii, 318 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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