Synopses & Reviews
Broad graduate-level survey of studies on invariant subspaces focuses on operators on separable Hilbert spaces. Prior knowledge of operators on Hilbert space unnecessary; geared toward mathematicians with a working knowledge of measure theory, complex analysis, and elementary functional analysis. Contents: Introduction and Preliminaries. 1. Normal Operators. 2. Analytic Functions of Operators. 3. Shift Operators. 4. Examples of Invariant Subspace Lattices. 5. Compact Operators. 6. Existence of Invariant and Hyperinvariant Subspaces. 7. Certain Results on von Neumann Algebras. 8. Transitive Operator Algebras. 9. Algebras Associated with Invariant Subspaces. 10. Some Unsolved Problems. References. List of Symbols. Indexes. New Appendix on Recent Developments. Revised and updated republication of the edition published by Springer-Verlag, Berlin, 1973.
Synopsis
Broad graduate-level survey of studies on invariant subspaces focuses on operators on separable Hilbert spaces. Prior knowledge of operators on Hilbert space unnecessary; geared toward mathematicians with a working knowledge of measure theory, complex analysis, and elementary functional analysis.
Synopsis
Broad survey focuses on operators on separable Hilbert spaces. Topics include normal operators, analytic functions of operators, shift operators, invariant subspace lattices, compact operators, invariant and hyperinvariant subspaces, more. 1973 edition.
Synopsis
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.
Table of Contents
Introduction and Preliminaries
1. Normal Operators
2. Analytic Functions of Operators
3. Shift Operators
4. Examples of Invariant Subspace Lattices
5. Compact Operators
6. Existence of Invariant and Hyperinvariant Subspaces
7. Certain Results on von Neumann Algebras
8. Transitive Operator Algebras
9. Algebras Associated with Invariant Subspaces
10. Some Unsolved Problems
References. List of Symbols. Indexes. New Appendix on Recent Developments