Junge M. Mixed-norm inequalities and operator space Lρ embedding theory / Junge M., Parcet J. - Providence: American Mathematical Society, 2010. - 155 p. - (Memoirs of the American Mathematical Society; Vol.203, N 953). - Bibliogr.: p.153-155. - Ind.: p.171-172. - ISBN 978-0-8218-4655-1; ISSN 0065-9266 - ISBN 978-90-5948-3  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Introduction .................................................... 1 0.1. Noncommutative function spaces ............................. 2 0.2. Amalgamated Lp spaces ...................................... 3 0.3. Conditional Lp spaces ...................................... 5 0.4. Intersection spaces ........................................ 7 0.5. Mixed-norm inequalities .................................... 8 0.6. Operator space Lp embeddings ............................... 9 Chapter 1. Noncommutative integration .......................... 13 1.1. Noncommutative Lp spaces .................................. 13 1.2. Pisier's vector-valued Lp spaces .......................... 17 1.3. The spaces Lpr(, E) and Lpc(, E) ...................... 20 Chapter 2. Amalgamated Lp spaces ............................... 27 2.1. Haagerup's construction ................................... 29 2.2. Triangle inequality on ∂∞ K ............................... 31 2.3. A metric structure on the solid К ......................... 38 Chapter 3. An interpolation theorem ............................ 43 3.1. Finite von Neumann algebras ............................... 44 3.2. Conditional expectations on ∂∞ K .......................... 48 3.3. General von Neumann algebras I ............................ 55 3.4. General von Neumann algebras II ........................... 61 3.5. Proof of the main interpolation theorem ................... 66 Chapter 4. Conditional Lp spaces ............................... 71 4.1. Duality ................................................... 72 4.2. Conditional L∞ spaces ..................................... 73 4.3. Interpolation results and applications .................... 74 Chapter 5. Intersections of Lp spaces .......................... 79 5.1. Free Rosenthal inequalities ............................... 79 5.2. Estimates for BMO type norms .............................. 83 5.3. Interpolation of 2-term intersections ..................... 99 5.4. Interpolation of 4-term intersections .................... 103 Chapter 6. Factorization of np,q(, E) ...................... 107 6.1. Amalgamated tensors ...................................... 108 6.2. Conditional expectations and ultraproducts ............... 112 6.3. Factorization of the space n∞,1(, E) ................. 115 Chapter 7. Mixed-norm inequalities ........................... 119 7.1. Embedding of np,q(, E) into Lp(; ℓqn) ............... 119 7.2. Asymmetric Lp spaces and noncommutative (∑pq) ............ 126 Chapter 8. Operator space Lp embeddings ....................... 129 8.1. Embedding Schatten classes ............................... 129 8.2. Embedding into the hyperfinite factor .................... 132 8.3. Embedding for general von Neumann algebras ............... 144 8.1. Bibliography ............................................. 153