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Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory
 
Marius Junge University of Illinois at Urbana-Champaign, Urbana, IL
Javier Parcet Instituto de Ciencias Mathemáticas CSIC-UAM-UC3M-UCM, Madrid, Spain
Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory
eBook ISBN:  978-1-4704-0567-0
Product Code:  MEMO/203/953.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory
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Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory
Marius Junge University of Illinois at Urbana-Champaign, Urbana, IL
Javier Parcet Instituto de Ciencias Mathemáticas CSIC-UAM-UC3M-UCM, Madrid, Spain
eBook ISBN:  978-1-4704-0567-0
Product Code:  MEMO/203/953.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2032009; 155 pp
    MSC: Primary 46

    Let \(f_1, f_2, \ldots, f_n\) be a family of independent copies of a given random variable \(f\) in a probability space \((\Omega, \mathcal{F}, \mu)\). Then, the following equivalence of norms holds whenever \(1 \le q \le p < \infty\), \[ \left( \int_{\Omega} \left[ \sum_{k=1}^n |f_k|^q \right]^{p/q} d \mu \right)^{1/p} \sim \max_{r \in \{p,q\}} \left\{ n^{1/r} \left( \int_\Omega |f|^r d\mu \right)^{1/r} \right\}.\] The authors prove a noncommutative analogue of this inequality for sums of free random variables over a given von Neumann subalgebra. This formulation leads to new classes of noncommutative function spaces which appear in quantum probability as square functions, conditioned square functions and maximal functions.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Noncommutative integration
    • 2. Amalgamated $L_p$ spaces
    • 3. An interpolation theorem
    • 4. Conditional $L_p$ spaces
    • 5. Intersections of $L_p$ spaces
    • 6. Factorization of $\mathcal {J}_{p,q}^n(\mathcal {M}, \mathsf {E})$
    • 7. Mixed-norm inequalities
    • 8. Operator space $L_p$ embeddings
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2032009; 155 pp
MSC: Primary 46

Let \(f_1, f_2, \ldots, f_n\) be a family of independent copies of a given random variable \(f\) in a probability space \((\Omega, \mathcal{F}, \mu)\). Then, the following equivalence of norms holds whenever \(1 \le q \le p < \infty\), \[ \left( \int_{\Omega} \left[ \sum_{k=1}^n |f_k|^q \right]^{p/q} d \mu \right)^{1/p} \sim \max_{r \in \{p,q\}} \left\{ n^{1/r} \left( \int_\Omega |f|^r d\mu \right)^{1/r} \right\}.\] The authors prove a noncommutative analogue of this inequality for sums of free random variables over a given von Neumann subalgebra. This formulation leads to new classes of noncommutative function spaces which appear in quantum probability as square functions, conditioned square functions and maximal functions.

  • Chapters
  • Introduction
  • 1. Noncommutative integration
  • 2. Amalgamated $L_p$ spaces
  • 3. An interpolation theorem
  • 4. Conditional $L_p$ spaces
  • 5. Intersections of $L_p$ spaces
  • 6. Factorization of $\mathcal {J}_{p,q}^n(\mathcal {M}, \mathsf {E})$
  • 7. Mixed-norm inequalities
  • 8. Operator space $L_p$ embeddings
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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