This book presents nine survey articles addressing topics surrounding positivity, with an emphasis on functional analysis. The book assembles a wide spectrum of research into positivity, providing up-to-date information on topics of current interest. The discussion provides insight into classical areas like spaces of continuous functions, f-algebras, and integral operators. The coverage extends is broad, including vector measures, operator spaces, ordered tensor products, and non-commutative Banach function spaces.
Author(s): Karim Boulabiar, Gerard Buskes, Abdelmajid Triki
Edition: 1
Year: 2007
Language: English
Pages: 282
Cover......Page 1
Trends in Mathematics......Page 3
Positivity......Page 4
Copyright - ISBN: 3764384778......Page 5
Contents......Page 6
Preface......Page 7
Ways in which C(X) mod a Prime Ideal Can be a Valuation Domain; Something Old and Something New......Page 8
Positivity in Operator Algebras and Operator Spaces......Page 33
1. Introduction......Page 78
2. Averaging operators......Page 79
3. Square-mean closed and geometric-mean closed f-algebras......Page 85
4. Maximal rings of quotients and (extended) orthomorphisms......Page 90
5. Order bounded disjointness preserving operators......Page 93
6. A new representation theorem......Page 96
References......Page 99
1. Introduction and terminology......Page 102
2. Fremlin’s tensor product......Page 106
2.1. Bilinear maps of order bounded variation......Page 107
2.3. Bilinear maps of bounded semivariation......Page 108
2.4. Bilinear maps of bounded norm variation......Page 109
2.5. Fremlin tensor product and bornologies......Page 110
3. The adjoints of bilinear maps......Page 112
4. Arens regular maps......Page 113
5. Orthosymmetric maps......Page 114
6.1. Squares......Page 115
6.2. Higher powers......Page 116
8. Disjointness preserving bilinear operators......Page 118
9. Injective and projective tensor product......Page 120
10. RNP for Tensor Products......Page 123
References......Page 127
Vector Measures, Integration and Applications......Page 132
The Role of Frames in the Development of Lattice-ordered Groups: A Personal Account......Page 166
Non-commutative Banach Function Spaces......Page 201
Positive Operators on Lp-spaces......Page 232
Regular Operators between Banach Lattices......Page 258
