Preface p. vii
Introduction p. 1
1 Spectra of Bounded Linear Operators p. 11
1.1 The spectrum of a bounded linear operator p. 11
1.2 Compact and [alpha]-contractive linear operators p. 16
1.3 Subdivision of the spectrum p. 23
1.4 Essential spectra of bounded linear operators p. 30
1.5 Notes, remarks and references p. 33
2 Some Characteristics of Nonlinear Operators p. 40
2.1 Some metric characteristics of nonlinear operators p. 40
2.2 A list of examples p. 43
2.3 Compact and [alpha]-contractive nonlinear operators p. 51
2.4 Special subsets of scalars p. 61
2.5 Notes, remarks and references p. 64
3 Invertibility of Nonlinear Operators p. 67
3.1 Proper and ray-proper operators p. 67
3.2 Coercive and ray-coercive operators p. 73
3.3 Further properties of nonlinear operators p. 76
3.4 The mapping spectrum p. 78
3.5 Excursion: topological degree theory p. 85
3.6 Notes, remarks and references p. 92
4 The Rhodius and Neuberger Spectra p. 94
4.1 The Rhodius spectrum p. 94
4.2 Frechet differentiable operators p. 96
4.3 The Neuberger spectrum p. 100
4.4 Special classes of operators p. 103
4.5 Notes, remarks and references p. 107
5 The Kachurovskij and Dorfner Spectra p. 109
5.1 Lipschitz continuous operators p. 109
5.2 The Kachurovskij spectrum p. 111
5.3 The Dorfner spectrum p. 118
5.4 Restricting the Kachurovskij spectrum p. 120
5.5 Semicontinuity properties of spectra p. 121
5.6 Continuity properties of resolvent operators p. 123
5.7 Notes, remarks and references p. 125
6 The Furi-Martelli-Vignoli Spectrum p. 130
6.1 Stably solvable operators p. 130
6.2 FMV-regular operators p. 135
6.3 The FMV-spectrum p. 139
6.4 Subdivision of the FMV-spectrum p. 141
6.5 Special classes of operators p. 144
6.6 The AGV-spectrum p. 148
6.7 Notes, remarks and references p. 155
7 The Feng Spectrum p. 159
7.1 Epi and k-epi operators p. 159
7.2 Feng-regular operators p. 166
7.3 The Feng spectrum p. 170
7.4 Special classes of operators p. 173
7.5 A comparison of different spectra p. 178
7.6 Notes, remarks and references p. 181
8 The Vath Phantom p. 184
8.1 Strictly epi operators p. 184
8.2 The phantom and the large phantom p. 186
8.3 The point phantom p. 192
8.4 Special classes of operators p. 199
8.5 A comparison of spectra and phantoms p. 206
8.6 Notes, remarks and references p. 212
9 Other Spectra p. 214
9.1 The semilinear Feng spectrum p. 214
9.2 The semilinear FMV-spectrum p. 223
9.3 The pseudo-adjoint spectrum p. 228
9.4 The Singhof-Weyer spectrum p. 232
9.5 The Weber spectrum p. 240
9.6 Spectra for homogeneous operators p. 243
9.7 The Infante-Webb spectrum p. 253
9.8 Notes, remarks and references p. 263
10 Nonlinear Eigenvalue Problems p. 268
10.1 Classical eigenvalues p. 268
10.2 Eigenvalue problems in cones p. 275
10.3 A nonlinear Krejn-Rutman theorem p. 280
10.4 Other notions of eigenvalue p. 285
10.5 Connected eigenvalues p. 294
10.6 Notes, remarks and references p. 296
11 Numerical Ranges of Nonlinear Operators p. 303
11.1 Linear operators in Hilbert spaces p. 303
11.2 Linear operators in Banach spaces p. 307
11.3 Numerical ranges of nonlinear operators p. 313
11.4 Numerical ranges and Jordan domains p. 327
11.5 Notes, remarks and references p. 329
12 Some Applications p. 336
12.1 Solvability of nonlinear equations p. 336
12.2 Solvability of semilinear equations p. 341
12.3 Applications to boundary value problems p. 350
12.4 Bifurcation and asymptotic bifurcation points p. 360
12.5 The p-Laplace operator p. 366
12.6 Notes, remarks and references p. 369
References p. 375
List of Symbols p. 395
Index p. 401