Author | Kubrusly, Carlos S. author |
---|---|
Title | Hilbert Space Operators [electronic resource] : A Problem Solving Approach / by Carlos S. Kubrusly |
Imprint | Boston, MA : Birkhรคuser Boston, 2003 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2064-0 |
Descript | XIII, 149 p. online resource |
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 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 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 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 Strongly Stable -- 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 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 Hildenโs 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