Putnam, C: Commutation Properties of Hilbert Space Operators

< ?) degrees of freedom.- 4.12 Anticommutation relations.- 4.13 General systems.- 4.14 A uniqueness theorem.- 4.15 Existence of the vacuum state.- 4.16 Self-adjointness of ?A?*A?.- 4.17 Remarks on commutators and the equations of motion.- V. Wave operators and unitary equivalence of self-adjoint operators.- 5.1 Introduction and a basic theorem.- 5.2 Schmidt and trace classes.- 5.3 Some lemmas.- 5.4 One-dimensional perturbations.- 5.5 Perturbations by operators of trace class.- 5.6 Invariance of wave operators.- 5.7 Generalizations.- 5.8 Applications to differential operators.- 5.9 A sufficient condition for the existence of W±(H1, H0).- 5.10 Hamiltonian operators.- 5.11 Existence of W± for the Hamiltonian case.- 5.12 A criterion for self-adjointness of perturbed operators.- 5.13 Existence and properties of wave and scattering operators.- 5.14 Stationary approach to scattering.- 5.15 Non-negative perturbations.- 5.16 Hamiltonians and non-negative perturbations.- 5.17 Remarks on unitary equivalence.- VI. Laurent and Toeplitz operators, singular integral operators and Jacobi matrices.- 6.1 Laurent and Toeplitz operators.- 6.2 A spectral inclusion theorem.- 6.3 A special Toeplitz matrix.- 6.4 Spectra of self-adjoint Toeplitz operators.- 6.5 Two lemmas.- 6.6 Analytic and coanalytic Toeplitz operators.- 6.7 Absolute continuity of Toeplitz operators.- 6.8 Spectral resolutions for certain Toeplitz operators.- 6.9 Some results for unbounded operators.- 6.10 Hilbert matrix.- 6.11 Singular integral operators.- 6.12 A(h, ?, E) with E bounded.- 6.13 The norm of A(0, ?, E).- 6.14 An estimate of meas sp (A(h, ?, E)).- 6.15 Remarks.- 6.16 Absolute continuity.- 6.17 Other singular integrals.- 6.18 Reducing spaces of A(0, ?, E).- 6.19 Estimates for ?? and ??.- 6.20 Spectral representation for A(0,1, (a, b)).- 6.21 Remarks on the spectra of singular integral operators.- 6.22 Jacobi matrices and absolute continuity.- Symbol Index.- Author Index.