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Tables of Contents for An Introduction to Local Spectral Theory
Chapter/Section Title
Page #
Page Count
Decomposable operators
1
98
The evolution of axiomatic spectral theory
1
6
Characterizations of decomposability
7
27
Distinguished parts of the spectrum
34
4
Super-decomposable operators
38
16
Generalized scalar operators
54
22
Local spectral properties of isometries and shifts
76
14
Growth conditions and Bishop's property (β)
90
7
Summary of local spectral properties
97
1
Functional models, duality theory, and invariant subspaces
98
99
Tensor products and analytic functions
99
13
The three-space lemmas for properties (β) and (δ)
112
8
Interlude on Bergman and Sobolev-type spaces
120
14
Decomposable extensions and liftings
134
15
The duality between property (β) and property (δ)
149
25
Existence of invariant subspaces
174
23
The spectrum and spectral inclusions
197
102
The Kato spectrum
199
12
The Allan--Leiterer theory
211
9
Spectral subspaces
220
23
Local spectral inclusions and permanence properties
243
12
Perturbed spectral inclusions
255
15
Local spectral properties of commutators
270
14
Fredholm theory and essential spectra
284
15
Local spectral theory for multipliers
299
167
Multipliers on commutative Banach algebras
300
18
Permanence properties of decomposable multipliers
318
11
Regular algebras and the hull-kernel topology
329
19
Decomposable multiplication operators
348
14
Multipliers in Mo(A) and Moo(A)
362
6
Natural spectrum and symmetric algebras
368
9
Natural local spectra and Tauberian algebras
377
9
Banach algebras with scattered or discrete spectra
386
10
Compact and Riesz multipliers
396
9
Multipliers with closed range
405
16
Decomposable convolution operators
421
13
Arveson spectrum and spectral mapping theorems
434
18
Banach algebras of vector-valued functions
452
14
Connections to automatic continuity
466
67
Some basic principles of automatic continuity
467
9
Translation-invariance and causality
476
7
Singularity points for mappings of local type
483
11
Intertwining linear transformations
494
11
Non-analytic functional calculi
505
15
Homomorphisms and derivations on Co(Ω.A)
520
13
Open problems
533
7
Operator theory
533
3
Banach algebras and multipliers
536
3
Automatic continuity
539
1
Appendix
540
9
A.1 Basic functional analysis
540
4
A.2 Banach algebras
544
3
A.3 Vector-valued analytic functions
547
2
Bibliography
549
26
Index of notation
575
2
Index
577