Invariant subspaces 不变子空间

While this broad survey comprises numerous studies on invariant subspaces, the authors have restricted the focus to operators on separate Hilbert space. Largely self-contained, the work requires no prior serious study of operators on Hilbert space and is well within the grasp of mathematicians with 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.Subsequent chapters cover certain results on von Neumann lgebras,transitive operator algebras, algebras associated with invariant subspaces, and a selection of unsolved problems.
Each chapter contains a list of results closely related to the material discussed and provable by methods similar to those employed in the text, offering students the option of a variety of supplementary problems to expand their understanding.

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
3.2 Invariant Subspaces of Shifts of Multiplicity
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 Sfims
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 LatA
5.3 Spectrum and LatA
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 of
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
……
Chapter 10. Some Unsolved Problems
Chapter 11. Some Subequent Developments
Additional References