Invariant Subspaces

Name: Invariant Subspaces
Brand: Dover Publications
Price: 29.49 EUR
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Heydar Radjavi(Autor*in)

Dover Publications (Verlag)

Erschienen am 30. November 2011

520 Seiten

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978-0-486-15302-5 (ISBN)

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Inhalt

Cover
Title Page
Dedication
Copyright Page
Preface to the Second Edition
Preface
Contents
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 8. Transitive Operator Algebras
8.1 Strictly Transitive Algebras
8.2 Partial Solutions of the Transitive Algebra Problem
8.3 Generators
8.4 Additional Propositions
8.5 Notes and Remarks
Chapter 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
Chapter 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
Subject Index
Chapter 11. Some Subsequent Developments
11.1 Normal Operators
11.2 Attainable Lattices
11.3 Existence of Invariant Subspaces
11.4 Reducing Subspaces and von Neumann algebras
11.5 Transitive and Reductive Algebras
11.6 Reflexive Algebras
11.7 Triangular Operator Algebras
Additional References

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