Author | Radjavi, Heydar. author |
---|---|
Title | Invariant Subspaces [electronic resource] / by Heydar Radjavi, Peter Rosenthal |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1973 |
Connect to | http://dx.doi.org/10.1007/978-3-642-65574-6 |
Descript | XII, 222 p. online resource |
0. Introduction and Preliminaries -- 0.1 Hilbert Space -- 0.2 Invariant Subspaces -- 0.3 Spectra of Operators -- 0.4 Linear Operator Equations -- 0.5 Additional Propositions -- 0.6 Notes and Remarks -- 1. Normal Operators -- 1.1 Preliminaries -- 1.2 Compact Normal Operators -- 1.3 Spectral TheoremโFirst Form -- 1.4 Spectral TheoremโSecond Form -- 1.5 Fugledeโs Theorem -- 1.6 The Algebra ?? -- 1.7 The Functional Calculus -- 1.8 Completely Normal Operators -- 1.9 Additional Propositions -- 1.10 Notes and Remarks -- 2. Analytic Functions of Operators -- 2.1 The Functional Calculus -- 2.2 The Riesz Decomposition Theorem -- 2.3 Invariant Subspaces of Analytic Functions of Operators -- 2.4 Additional Propositions -- 2.5 Notes and Remarks -- 3. Shift Operators -- 3.1 Shifts of Multiplicity 1 -- 3.2 Invariant Subspaces of Shifts of Multiplicity 1 -- 3.3 Shifts of Arbitrary Multiplicity -- 3.4 Invariant Subspaces of Shifts -- 3.5 Parts of Shifts -- 3.6 Additional Propositions -- 3.7 Notes and Remarks -- 4. Examples of Invariant Subspace Lattices -- 4.1 Preliminaries -- 4.2 Algebraic Operators -- 4.3 Lattices of Normal Operators -- 4.4 Two Unicellular Operators -- 4.5 Direct Products of Attainable Lattices -- 4.6 Attainable Ordinal Sums -- 4.7 Transitive Lattices -- 4.8 Additional Propositions -- 4.9 Notes and Remarks -- 5. Compact Operators -- 5.1 Existence of Invariant Subspaces -- 5.2 Normality and Lat A -- 5.3 Spectrum and Lat A -- 5.4 Lattices of Compact Operators -- 5.5 Additional Propositions -- 5.6 Notes and Remarks -- 6. Existence of Invariant and Hyperinvariant Subspaces -- 6.1 Operators on Other Spaces -- 6.2 Perturbations of Normal Operators -- 6.3 Quasi-similarity and Invariant Subspaces -- 6.4 Hyperinvariant Subspaces -- 6.5 Additional Propositions -- 6.6 Notes and Remarks -- 7. Certain Results on von Neumann Algebras -- 7.1 Preliminaries -- 7.2 Commutants -- 7.3 The Algebra ? (?) -- 7.4 Abelian von Neumann Algebras -- 7.5 The Class of n-normal Operators -- 7.6 Additional Propositions -- 7.7 Notes and Remarks -- 8. Transitive Operator Algebras -- 8.1 Strictly Transitive Algebras -- 8.2 Partial Solutions of the Transitive Algebra Problem -- 8.3 Generators of ? (?) -- 8.4 Additional Propositions -- 8.5 Notes and Remarks -- 9. Algebras Associated with Invariant Subspaces -- 9.1 Reductive Algebras -- 9.2 Reflexive Operator Algebras -- 9.3 Triangular Operator Algebras -- 9.4 Additional Propositions -- 9.5 Notes and Remarks -- 10. Some Unsolved Problems -- 10.1 Normal Operators -- 10.2 Attainable Lattices -- 10.3 Existence of Invariant Subspaces -- 10.4 Reducing Subspaces and von Neumann Algebras -- 10.5 Transitive and Reductive Algebras -- 10.6 Reflexive Algebras -- 10.7 Triangular Algebras -- References -- List of Symbols -- Author Index