Muller V. Spectral theory of linear operators and spectral systems in Banach algebras (Basel, 2007). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаMüller V. Spectral theory of linear operators and spectral systems in Banach algebras. - 2nd ed. - Basel: Birkhauser Verlag, 2007. - 439 p. - (Operator theory, advances and applications; Vol. 139). - ISBN 3764382643; ISBN 9783764382643
 

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Оглавление / Contents
 
Preface	 ...................................................... vii

Preface to the Second Edition ................................. ix

I.   Banach Algebras
     1.  Basic Concepts ......................................... 1
     2.  Commutative Banach algebras ........................... 18
     3.  Approximate point spectrum in commutative
         Banach algebras ....................................... 26
     4.  Permanently singular elements and removability
         of spectrum ........................................... 34
     5.  Non-removable ideals .................................. 42
     6.  Axiomatic theory of spectrum .......................... 51
     7.  Spectral systems ...................................... 58
     8.  Basic spectral systems in Banach algebras ............. 68
     Comments on Chapter I ..................................... 72

II.  Operators
     9.  Spectrum of operators ................................. 85
     10. Operators with closed range ........................... 97
     11. Factorization of vector-valued functions ............. 106
     12. Kato operators ....................................... 117
     13. General inverses and Saphar operators ................ 130
     14. Local spectrum ....................................... 135
     Comments on Chapter II ................................... 143

III. Essential Spectrum
     15. Compact operators .................................... 149
     16. Fredholm and semi-Fredholm operators ................. 155
     17. Construction of Sadovskii/Buoni, Harte, Wickstead .... 164
     18. Perturbation properties of Fredholm and
         semi-Fredholm operators .............................. 169
     19. Essential spectra .................................... 172
     20. Ascent, descent and Browder operators ................ 178
     21. Essentially Kato operators ........................... 187
     22. Classes of operators defined by means of kernels
         and ranges ........................................... 197
     23. Semiregularities and miscellaneous spectra ........... 211
     24. Measures of non-compactness and other operator
         quantities ........................................... 220
     Comments on Chapter III .................................. 228

IV.  Taylor Spectrum
     25. Basic properties ..................................... 237
     26. Split spectrum    .................................... 245
     27. Some non-linear results .............................. 252
     28. Taylor functional calculus for the split spectrum .... 260
     29. Local spectrum for n-tuples of operators ............. 266
     30. Taylor functional calculus ........................... 271
     31. Taylor functional calculus in Banach algebras ........ 283
     32. k-regular functions .................................. 285
     33. Stability of index of complexes ...................... 293
     34. Essential Taylor spectrum ............................ 299
     Comments on Chapter IV ................................... 305

V.   Orbits and Capacity
     35. Joint spectral radius ................................ 311
     36. Capacity ............................................. 321
     37. Invariant subset problem and large orbits ............ 327
     38. Hypercyclic vectors .................................. 341
     39. Weak orbits .......................................... 348
     40. Scott Brown technique ................................ 359
     41. Kaplansky's type theorems ............................ 375
     42. Polynomial orbits and local capacity ................. 378
     Comments on Chapter V .................................... 387

Appendix ...................................................... 393
A.l. Banach spaces ............................................ 393
A.2. Analytic vector-valued functions ......................... 398
A.3. C-functions ............................................. 401
A.4. Semicontinuous set-valued functions ...................... 403
A.5. Some geometric properties of Banach spaces ............... 404
A.6. Basic properties of H ................................... 405

Bibliography .................................................. 407

Index ......................................................... 429

List of Symbols ............................................... 437


 
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