Simultaneous Triangularization - Brossura

Radjavi, Heydar

Brossura

ISBN 10: 0387984666 ISBN 13: 9780387984667

Casa editrice: Springer, 2013

Riassunto

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.

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Contenuti

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.

Product Description

Book by Radjavi Heydar Rosenthal Peter

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 0387984666
• ISBN 13: 9780387984667
• Rilegatura: Copertina flessibile
• Numero di pagine: 332
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania