Author | Radjavi, Heydar. author |
---|---|
Title | Simultaneous Triangularization [electronic resource] / by Heydar Radjavi, Peter Rosenthal |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1200-3 |
Descript | XII, 319 p. online resource |
One: Algebras of Matrices -- 1.1 The Triangularization Lemma -- 1.2 Burnsideโs 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 Lomonosovโs Lemma and McCoyโs 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