Heydar Radjavi

Invariant Subspaces (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces, and a selection of unsolved problems. 1973 edition. New appendix on recent developments.

Produktdetails

• Verlag: Dover Publications
• Erscheinungstermin: 30. November 2011
• Englisch
• ISBN-13: 9780486153025
• Artikelnr.: 40289494

Inhaltsangabe

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 Theorem-First Form.- 1.4 Spectral Theorem-Second Form.- 1.5 Fuglede's 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 NeumannAlgebras.- 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.