| Introduction | |
| Operator theory in finite-dimensional vector spaces | |
| Vector spaces and normed vector spaces | p. 1 |
| Linear forms and the adjoint space | p. 10 |
| Linear operators | p. 16 |
| Analysis with operators | p. 25 |
| The eigenvalue problem | p. 34 |
| Operators in unitary spaces | p. 47 |
| Perturbation theory in a finite-dimensional space | p. 62 |
| Analytic perturbation of eigenvalues | p. 63 |
| Perturbation series | p. 74 |
| Convergence radii and error estimates | p. 88 |
| Similarity transformations of the eigenspaces and eigenvectors | p. 98 |
| Non-analytic perturbations | p. 106 |
| Perturbation of symmetric operators | p. 120 |
| Introduction to the theory of operators in Banach spaces | |
| Banach spaces | p. 127 |
| Linear operators in Banach spaces | p. 142 |
| Bounded operators | p. 149 |
| Compact operators | p. 157 |
| Closed operators | p. 163 |
| Resolvents and spectra | p. 172 |
| Stability theorems | |
| Stability of closedness and bounded invertibility | p. 189 |
| Generalized convergence of closed operators | p. 197 |
| Perturbation of the spectrum | p. 208 |
| Pairs of closed linear manifolds | p. 218 |
| Stability theorems for semi-Fredholm operators | p. 229 |
| Degenerate perturbations | p. 244 |
| Operators in Hilbert spaces | |
| Hilbert space | p. 251 |
| Bounded operators in Hilbert spaces | p. 256 |
| Unbounded operators in Hilbert spaces | p. 267 |
| Perturbation of selfadjoint operators | p. 287 |
| The Schrodinger and Dirac operators | p. 297 |
| Sesquilinear forms in Hilbert spaces and associated operators | |
| Sesquilinear and quadratic forms | p. 308 |
| The representation theorems | p. 322 |
| Perturbation of sesquilinear forms and the associated operators | p. 336 |
| Quadratic forms and the Schrodinger operators | p. 343 |
| The spectral theorem and perturbation of spectral families | p. 353 |
| Analytic perturbation theory | |
| Analytic families of operators | p. 365 |
| Holomorphic families of type (A) | p. 375 |
| Selfadjoint holomorphic families | p. 385 |
| Holomorphic families of type (B) | p. 393 |
| Further problems of analytic perturbation theory | p. 413 |
| Eigenvalue problems in the generalized form | p. 416 |
| Asymptotic perturbation theory | |
| Strong convergence in the generalized sense | p. 427 |
| Asymptotic expansions | p. 441 |
| Generalized strong convergence of sectorial operators | p. 453 |
| Asymptotic expansions for sectorial operators | p. 463 |
| Spectral concentration | p. 473 |
| Perturbation theory for semigroups of operators | |
| One-parameter semigroups and groups of operators | p. 479 |
| Perturbation of semigroups | p. 497 |
| Approximation by discrete semigroups | p. 509 |
| Perturbation of continuous spectra and unitary equivalence | |
| The continuous spectrum of a selfadjoint operator | p. 516 |
| Perturbation of continuous spectra | p. 525 |
| Wave operators and the stability of absolutely continuous spectra | p. 529 |
| Existence and completeness of wave operators | p. 537 |
| A stationary method | p. 553 |
| Bibliography | p. 583 |
| Supplementary Bibliography | p. 596 |
| Notation index | p. 606 |
| Author index | p. 608 |
| Subject index | p. 612 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
