Mixed-Norm Inequalities and Operator Space L_{p} Embedding Theory.

Intro -- Contents -- Abstract -- Introduction -- 0.1. Noncommutative function spaces -- 0.2. Amalgamated Lp spaces -- 0.3. Conditional Lp spaces -- 0.4. Intersection spaces -- 0.5. Mixed-norm inequalities -- 0.6. Operator space Lp embeddings -- Chapter 1. Noncommutative integration -- 1.1. Noncommutative Lp spaces -- 1.2. Pisier's vector-valued Lp spaces -- 1.3. The spaces Lpr(M, E) and Lpc(M, E) -- Chapter 2. Amalgamated Lp spaces -- 2.1. Haagerup's construction -- 2.2. Triangle inequality on K -- 2.3. A metric structure on the solid K -- Chapter 3. An interpolation theorem -- 3.1. Finite von Neumann algebras -- 3.2. Conditional expectations on K -- 3.3. General von Neumann algebras I -- 3.4. General von Neumann algebras II -- 3.5. Proof of the main interpolation theorem -- Chapter 4. Conditional Lp spaces -- 4.1. Duality -- 4.2. Conditional L spaces -- 4.3. Interpolation results and applications -- Chapter 5. Intersections of Lp spaces -- 5.1. Free Rosenthal inequalities -- 5.2. Estimates for BMO type norms -- 5.3. Interpolation of 2-term intersections -- 5.4. Interpolation of 4-term intersections -- Chapter 6. Factorization of Jp,qn(M, E) -- 6.1. Amalgamated tensors -- 6.2. Conditional expectations and ultraproducts -- 6.3. Factorization of the space J,1n(M, E) -- Chapter 7. Mixed-norm inequalities -- 7.1. Embedding of Jp,qn(M, E) into Lp(A -- qn) -- 7.2. Asymmetric Lp spaces and noncommutative (pq) -- Chapter 8. Operator space Lp embeddings -- 8.1. Embedding Schatten classes -- 8.2. Embedding into the hyperfinite factor -- 8.3. Embedding for general von Neumann algebras -- Bibliography.

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