This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in the area and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, and functional analysis. The material is of interest to experts, young researchers and postgraduate students.
Author(s): Guillermo P. Curbera, Gerd Mockenhaupt, Werner J. Ricker
Series: Operator Theory: Advances and Applications
Edition: 1st Edition.
Publisher: Birkhäuser Basel
Year: 2010
Language: English
Pages: 397
Cover......Page 1
Series: Operator Theory: Advances and Applications Vol. 201......Page 3
Vector Measures, Integration and Related Topics......Page 4
Copyright Page - ISBN: 3034602103......Page 5
Table of Contents......Page 6
Preface......Page 10
List of Talks......Page 12
1. Introduction......Page 16
2. Preliminary results......Page 18
3. Mean ergodic results......Page 22
References......Page 34
0. Introduction......Page 36
1. Vector-valued Fourier series and operator-valued Fourier multipliers
......Page 37
2. The Marcinkiewicz multiplier theorem in the general case......Page 45
3. The periodic non-homogeneous problems......Page 46
4. Maximal regularity......Page 47
5. The non-autonomous equations......Page 51
References......Page 53
1. Introduction......Page 56
2.1. Definitions and notations......Page 57
2.2. The Berg-Maserick type theorem......Page 58
3. An integral representation via spectral measures......Page 59
4. Examples of ∗-representations......Page 60
5. A construction of the spectral measure......Page 62
6. The Gelfand-Naimark theorem for abelian C∗-algebras......Page 63
References......Page 64
1. Introduction and preliminaries......Page 66
2. The results......Page 68
References......Page 72
1. Introduction and preliminaries......Page 74
References......Page 79
1. Introduction......Page 80
2. Strong μ-normability of operator-valued functions......Page 82
3. Spaces of operator-valued functions......Page 87
References......Page 93
2. Preliminaries......Page 94
3. I-convergence in Riesz spaces......Page 96
4. Applications......Page 99
References......Page 101
1. Introduction......Page 104
2. Preliminaries......Page 105
3. Bochner integrable functions......Page 106
4. Pettis integrable functions......Page 109
References......Page 112
1. Introduction......Page 114
2. Preliminaries......Page 115
3. Separately disjointness preserving operators......Page 117
References......Page 122
1. Introduction......Page 124
2. Compactness and weak compactness......Page 125
References......Page 128
1. Introduction......Page 130
2. Multivalued integrals......Page 131
3. Results......Page 133
References......Page 138
1. Introduction......Page 140
2. Preliminaries......Page 141
3. Properties of the almost periodic functions......Page 143
4. Equations with almost periodic measures and functions......Page 145
References......Page 148
1. Introduction: a problem on vector measures......Page 150
2. The Rademacher system......Page 151
3. A problem on function spaces......Page 153
4.1. The space Λ(R,X)......Page 154
4.2. The symmetric kernel of Λ(R,X)......Page 156
4.3. When is Λ(R,X) rearrangement invariant?......Page 158
4.4. Head and tail behavior......Page 161
References......Page 162
1. Introduction......Page 164
2. Preliminaries......Page 165
3. R.i. optimal domain for T......Page 166
References......Page 172
1. Introduction......Page 174
2. Preliminaries......Page 175
3. A convergence theorem for the S_1-integral on the real line......Page 176
4. Product local system......Page 178
5. S-integral for a product local system......Page 179
6. The Fubini Theorem for a product local system......Page 181
References......Page 185
Introduction......Page 186
1. Notations and preliminaries......Page 187
2. A decomposition theorem for HKP-integrable multifunctions......Page 190
References......Page 196
1. Introduction and preliminaries......Page 198
2. Preliminaries and notation......Page 199
3.2. Symmetrically normed M-bimodules and their K¨othe duals......Page 202
3.3. Normal and singular functionals on a normed M-bimodule......Page 204
4. The Yosida-Hewitt decomposition in M-bimodules......Page 205
5. Elements of order-continuous norm and singular functionals......Page 207
6. A vector-valued Yosida-Hewitt theorem......Page 208
References......Page 212
Ideals of Subseries Convergence and Copies of c_0 in Banach Spaces......Page 214
References......Page 218
1. Introduction......Page 220
2. Measurable operator-valued functions......Page 221
2.1. Strongly p-integrable functions......Page 222
2.2. Classes of (operator-valued) integral multiplier functions......Page 224
2.3. (p, q)-integral functions......Page 225
2.4. A new class of operator-valued functions......Page 226
References......Page 229
1. Introduction......Page 230
2. Logarithms of measures and translations......Page 231
3. Logarithms of invertible isometries......Page 234
4. Trigonometrically well-bounded operators......Page 237
5. Trigonometrically well-bounded operators on super-reflexive
spaces and norm growth of iterates......Page 239
References......Page 243
0. Introduction......Page 246
1. Generalities......Page 247
2. 2-norm......Page 248
3. 3-norm......Page 250
4. H as an operator......Page 254
5. Further ideal properties......Page 255
References......Page 258
1. Introduction......Page 260
2. Review of the proof of the Tb theorem......Page 263
3. Probabilistic approach to the paraproduct......Page 264
References......Page 269
1. Introduction......Page 270
2. Bilinear integration in tensor products......Page 272
3. Random evolutions......Page 274
4. Scattering theory......Page 276
5. Bilinear integration with respect to white noise......Page 280
References......Page 284
1. Introduction......Page 286
2. Multiwavelets......Page 287
3. Multiwavelets with three taps......Page 289
4. Multiwavelets with four taps......Page 292
References......Page 298
1. Introduction......Page 300
2. Preliminaries......Page 301
3. Main results......Page 302
References......Page 307
Measure and Integration: Characterization of the New Maximal Contents and Measures
......Page 308
1.1 Lemma.......Page 309
1.4 Theorem.......Page 310
1.5 Example.......Page 311
2.3 Outer Remark.......Page 312
3. Another inner characterization theorem......Page 313
3.1 Theorem.......Page 314
3.3 Inner Characterization Theorem.......Page 315
4. Application to the inner measure constructions......Page 316
References......Page 317
1. Introduction......Page 318
2. Vector measures of bounded γ-variation......Page 319
References......Page 326
1. Introduction......Page 328
2. Proof of Theorem 1.1......Page 329
3. Weakly compact linear extension......Page 336
References......Page 337
A Note on R-boundedness in Bidual Spaces......Page 338
References......Page 340
1. Introduction......Page 342
2. p-adic Salem sets and the L^2-Fourier restriction phenomenon......Page 343
3. Optimal extension of the Hausdorff-Young inequality in Z_p......Page 349
References......Page 352
L-embedded Banach Spaces and a Weak Version of Phillips Lemma
......Page 354
References......Page 358
1.1. Complementability......Page 360
1.2. Notation......Page 362
1.3. Main result......Page 363
2.1. Recalling why c_0 is not complemented in l_∞......Page 364
2.2. Identifying measures and operators......Page 365
2.3. Rademacher functions......Page 366
2.4. Walsh system......Page 368
3. Proof in the non separable case......Page 371
References......Page 373
1. Introduction......Page 376
2. The L^0 case......Page 377
3. The Banach function space case......Page 379
4. Examples......Page 382
References......Page 384
1. Introduction......Page 386
2. Definitions and notation......Page 387
3. Example......Page 388
4. Non-negative scalar measures......Page 389
5. Vector measures......Page 390
6. Liapounoff convexity-type theorems......Page 392
References......Page 394
List of Participants......Page 396
