Hilbert Space Operators A Problem Solving Approach
This is a problem book on Hilbert space operators (Le. , on bounded linear transformations of a Hilbert space into itself) where theory and problems are investigated together. We tre!l:t only a part of the so-called single operator theory. Selected prob lems, ranging from standard textbook material...
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser
2003, 2003
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| Edition: | 1st ed. 2003 |
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Invariant Subspaces
- Problem 1.1 Closure
- Problem 1.2 Kernel and Range
- Problem 1.3 Null Product
- Problem 1.4 Operator Equation
- Problem 1.5 Nilpotent and Algebraic
- Problem 1.6 Polynomials
- Problem 1.7 Totally Cyclic
- Problem 1.8 Densely Intertwined
- Problem 1.9 Hyperinvariant
- Problem 1.10 Quasiaffine Transform
- Solutions
- 2 Hilbert Space Operators
- Problem 2.1 Adjoint
- Problem 2.2 Nonnegative
- Problem 2.3 Contraction
- Problem 2.4 Normal
- Problem 2.5 Isometry
- Problem 2.6 Unitary
- Problem 2.7 Projection
- Problem 2.8 Mutually Orthogonal
- Problem 2.9 Increasing
- Solutions
- 3 Convergence and Stability
- Problem 3.1 Diagonal
- Problem 3.2 Product
- Problem 3.3 * -Preserving
- Problem 3.4 Nonnegative
- Problem 3.5 Monotone
- Problem 3.6 Self-Adjoint
- Problem 3.7 Commutant
- Problem 3.8 Convex Cone
- Problem 3.9 Absolute Value
- Solutions
- 4 Reducing Subspaces
- Problem 4.1 T-Invariant
- Problem 4.2 Matrix Form
- Problem 8.15 Fuglede-Putnam Theorem
- Problem 8.16 Reducible
- Solutions
- 9 Paranormal Operators
- Problem 9.1 Quasihyponormal
- Problem 9.2 Semi-quasihyponormal
- Problem 9.3 Paranormal
- Problem 9.4 Square of Paranormal
- Problem 9.5 Alternative Definition
- Problem 9.6 Unitarily Equivalent
- Problem 9.7 Weighted Shift
- Problem 9.8 Equivalences
- Problem 9.9 Not Paranormal
- Problem 9.10 Projection ? Nilpotent
- Problem 9.11 Shifted Operators
- Problem 9.12 Shifted Projections
- Problem 9.13 Shifted Seif-Adjoints
- Problem 9.14 Examples
- Problem 9.15 Hyponormal
- Problem 9.16 Invertible
- Problem 9.17 Paranormal Inequality
- Problem 9.18 Normaloid
- Problem 9.19 Cohyponormal
- Problem 9.20 StronglyStable
- Problem 9.21 Quasinormal
- Solutions
- 10 Proper Contractions
- Problem 10.1 Equivalences
- Problem 10.2 Diagonal
- Problem 10.3 Compact
- Problem 10.4 Adjoint
- Problem 10.5 Paranormal
- Problem 10.6 Nagy-Foia? Classes
- Problem 6.13 Strongly Stable
- Problem 6.14 Property PF
- Problem 6.15 Direct Summand
- Solutions
- 7 Hyponormal Operators
- Problem 7.1 Quasinormal
- Problem 7.2 Strong Stability
- Problem 7.3 Hyponormal
- Problem 7.4 Direct Proof
- Problem 7.5 Invariant Subspace
- Problem 7.6 Restriction
- Problem 7.7 Normal
- Problem 7.8 Roots of Powers
- Problem 7.9 Normaloid
- Problem 7.10 Power Inequality
- Problem 7.11 Unitarily Equivalent
- Problem 7.12 Subnormal
- Problem 7.13 Not Subnormal
- Problem 7.14 Distinct Weights
- Solutions
- 8 Spectral Properties
- Problem 8.1 Spectrum
- Problem 8.2 Eigenspace
- Problem 8.3 Examples
- Problem 8.4 Residual Spectrum
- Problem 8.5 Weighted Shift
- Problem 8.6 Uniform Stability
- Problem 8.7 Finite Rank
- Problem 8.8 Stability for Compact
- Problem 8.9 Continuous Spectrum
- Problem 8.10 Compact Contraction
- Problem 8.11 Normal
- Problem 8.12 Square Root
- Problem 8.13 Fuglede Theorem
- Problem 8.14 Quasinormal
- Problem 4.3 T*-Invariant
- Problem 4.4 T and T*-Invariant
- Problem 4.5 Commuting with T and T*
- Problem 4.6 Reducible
- Problem 4.7 Restriction
- Problem 4.8 Direct Sum
- Problem 4.9 Unitarily Equivalent
- Problem 4.10 Unitary Restriction
- Solutions
- 5 Shifts
- Problem 5.1 Unilateral
- Problem 5.2 Bilateral
- Problem 5.3 Multiplicity
- Problem 5.4 Unitarily Equivalent
- Problem 5.5 Reducible
- Problem 5.6 Irreducible
- Problem 5.7 Rotation
- Problem 5.8 Riemann-Lebesgue Lemma
- Problem 5.9 Weighted Shift
- Problem 5.10 Nonnegative Weights
- Solutions
- 6 Decompositions
- Problem 6.1 Strong Limit
- Problem 6.2 Projection
- Problem 6.3 Kernels
- Problem 6.4 Kernel Decomposition
- Problem 6.5 Intertwined to Isometry
- Problem 6.6 Dual Limits
- Problem 6.7 Nagy-Foia?-Langer Decomposition
- Problem 6.8 von Neumann-Wold Decomposition.-Problem 6.9 Another Decomposition
- Problem 6.10 Foguel Decomposition
- Problem 6.11 Isometry
- Problem 6.12 Coisometry
- Problem 10.7 Weakly Stable
- Problem 10.8 Hyponormal
- Problem 10.9 Subnormal
- Problem 10.10 Quasinormal
- Problem 10.11 Direct Proof
- Problem 10.12 Invariant Subspace
- Solutions
- 11 Quasireducible Operators
- Problem 11.1 Alternative Definition
- Problem 11.2 Basic Properties
- Problem 11.3 Nilpotent
- Problem 11.4 Index 2
- Problem 11.5 Higher Indices
- Problem 11.6 Product
- Problem 11.7 Unitarily Equivalent
- Problem 11.8 Similarity
- Problem 11.9 Unilateral Shift
- Problem 11.10 Isometry
- Problem 11.11 Quasinormal
- Problem 11.12 Weighted Shift
- Problem 11.13 Subnormal
- Problem 11.14 Commutator
- Problem 11.15 Reducible
- Problem 11.16 Normal
- Solutions
- 12 The Lomonosov Theorem
- Problem 12.1 Hilden’s Proof
- Problem 12.2 Lomonosov Lemma
- Problem 12.3 Lomonosov Theorem
- Problem 12.4 Extension
- Problem 12.5 Quasireducible
- Problem 12.6 Hyponormal
- Solutions
- References