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| Introduction and Preliminaries | |
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| Hilbert Space | |
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| Invariant Subspaces | |
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| Spectra of Operators | |
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| Linear Operator Equations | |
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| Additional Propositions | |
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| Notes and Remarks | |
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| Normal Operators | |
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| Preliminaries | |
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| Compact Normal Operators | |
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| Spectral Theorem--First Form | |
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| Spectral Theorem--Second Form | |
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| Fuglede's Theorem | |
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| The Algebra L[superscript infinity] | |
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| The Functional Calculus | |
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| Completely Normal Operators | |
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| Additional Propositions | |
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| Notes and Remarks | |
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| Analytic Functions of Operators | |
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| The Functional Calculus | |
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| The Riesz Decomposition Theorem | |
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| Invariant Subspaces of Analytic Functions of Operators | |
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| Additional Propositions | |
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| Notes and Remarks | |
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| Shift Operators | |
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| Shifts of Multiplicity 1 | |
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| Invariant Subspaces of Shifts of Multiplicity 1 | |
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| Shifts of Arbitrary Multiplicity | |
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| Invariant Subspaces of Shifts | |
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| Parts of Shifts | |
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| Additional Propositions | |
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| Notes and Remarks | |
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| Examples of Invariant Subspace Lattices | |
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| Preliminaries | |
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| Algebraic Operators | |
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| Lattices of Normal Operators | |
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| Two Unicellular Operators | |
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| Direct Products of Attainable Lattices | |
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| Attainable Ordinal Sums | |
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| Transitive Lattices | |
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| Additional Propositions | |
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| Notes and Remarks | |
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| Compact Operators | |
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| Existence of Invariant Subspaces | |
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| Normality and Lat A | |
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| Spectrum and Lat A | |
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| Lattices of Compact Operators | |
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| Additional Propositions | |
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| Notes and Remarks | |
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| Existence of Invariant and Hyperinvariant Subspaces | |
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| Operators on Other Spaces | |
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| Perturbations of Normal Operators | |
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| Quasi-similarity and Invariant Subspaces | |
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| Hyperinvariant Subspaces | |
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| Additional Propositions | |
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| Notes and Remarks | |
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| Certain Results on von Neumann Algebras | |
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| Preliminaries | |
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| Commutants | |
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| The Algebra B (H) | |
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| Abelian von Neumann Algebras | |
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| The Class of n-normal Operators | |
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| Additional Propositions | |
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| Notes and Remarks | |
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| Transitive Operator Algebras | |
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| Strictly Transitive Algebras | |
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| Partial Solutions of the Transitive Algebra Problem | |
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| Generators of B (H) | |
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| Additional Propositions | |
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| Notes and Remarks | |
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| Algebras Associated with Invariant Subspaces | |
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| Reductive Algebras | |
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| Reflexive Operator Algebras | |
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| Triangular Operator Algebras | |
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| Additional Propositions | |
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| Notes and Remarks | |
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| Some Unsolved Problems | |
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| Normal Operators | |
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| Attainable Lattices | |
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| Existence of Invariant Subspaces | |
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| Reducing Subspaces and von Neumann Algebras | |
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| Transitive and Reductive Algebras | |
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| Reflexive Algebras | |
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| Triangular Algebras | |
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| References | |
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| List of Symbols | |
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| Author Index | |
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| Subject Index | |
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| Some Subsequent Developments | |
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| Normal Operators | |
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| Attainable Lattices | |
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| Existence of Invariant Subspaces | |
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| Reducing Subspaces and von Neumann algebras | |
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| Transitive and Reductive Algebras | |
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| Reflexive Algebras | |
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| Triangular Operator Algebras | |
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| Additional References | |