Advanced Courses of Mathematical Analysis I: Proceedings of the First International School

A. Aizpuru-Tomas, F. Leon-Saavedra9789812560605, 981-256-060-2

This volume consists of a collection of articles from experts with a rich research and educational experience. The contributors of this volume are: Y Benyamini, M Gonzбlez, V Mьller, S Reich, E Matouskova, A J Zaslavski and A R Palacios. Each of their work is invaluable. For example, Benyamini’s is the only updated survey of the exciting and active area of the classification of Banach spaces under uniformly continuous maps while Gonzбlez’s article is a pioneer introduction to the theory of local duality for Banach spaces.

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Table of contents :
Contents……Page 8
1. Introduction……Page 10
2. A General Overview……Page 12
3. Lipschitz Maps……Page 20
4. Uniformly Continuous Maps……Page 30
References……Page 36
Introduction…….Page 40
1. Basic properties……Page 43
2. Some characterizations……Page 44
3. Symmetry……Page 47
4. Some natural examples……Page 48
5. Spaces with a basis……Page 51
6. Further properties……Page 53
7. Tensor products……Page 54
8. Ultrapowers of Banach spaces……Page 56
9. Appendix: Ultrafilters……Page 58
References……Page 59
1. Introduction……Page 62
2. Regular orbits……Page 65
3. Hypercyclic vectors……Page 71
4. Weak orbits……Page 75
5. Polynomial orbits……Page 77
6. Capacity……Page 79
7. Scott Brown technique……Page 80
References……Page 87
Genericity in Nonexpansive Mapping Theory E. Matouikovci, S. Reach and A . J . Zaslavski……Page 90
2. Porous sets……Page 91
3. Null sets……Page 93
4. Nonexpansive and contractive mappings……Page 96
5. The set of contractive mappings contains a residual subset……Page 98
6. The complement of the set of contractive mappings is a-porous……Page 100
7. Well-posedness……Page 102
8. Strict contractions……Page 103
References……Page 105
Introduction……Page 108
1.1. Some basic definitions and facts……Page 109
1.2. Quaternions and Octonions……Page 111
1.3. The pioneering work of Ostrowski, Mazur, Albert, and Wright……Page 113
1.4. Classification……Page 116
2.1. The noncommutative Urbanik- Wright theorem……Page 118
2.2, Kaplansky ‘s prophetic proof of the noncommutative Urbanik- Wright theorem……Page 119
2.3. The commutative Urbanik- Wright theorem……Page 121
2.4. Power-associativity……Page 122
2.5. Flexibility……Page 125
2.6. H*-theory……Page 127
2.7. Alge braicity……Page 128
3.1. The basic examples……Page 131
3.2. Free normed nonassociative algebras……Page 133
3.3. Center, centroid, and extended centroid……Page 137
3.4. Algebras with involution……Page 138
3.5. One-sided division algebras……Page 142
3.6. Automatic continuity……Page 147
4.1. Nearly absolute-valued algebras……Page 150
4.2. Other deviations……Page 152
5.1. The isometric point of view……Page 153
5.2. The isomorphic point of view……Page 156
References……Page 159