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UMD property for Banach spaces and operator spaces

Yanqi Qiu 1
1 AF - Analyse fonctionnelle
IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
Abstract : This thesis presents some results on the local theory of Banach spaces and operator spaces. The first part consists of the study of the $\text{OUMD}$ property for the column Hilbert space $C$. In the second part we treat the classical $\text{UMD}$ property for Banach spaces. We give estimates of the $\text{UMD}$ constants for iterated $L_p(L_q)$ spaces. The main result yields a new and very natural construction of a family of super-reflexive and non-$\text{UMD}$ Banach lattices: The space $L_p(L_q(L_p(L_q(\cdots$ iterated infinitely many times is super-reflexive if $1 < p, q <\infty$ but is not $\text{UMD}$ if $ p \ne q$.
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  • HAL Id : tel-00794951, version 1

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Yanqi Qiu. UMD property for Banach spaces and operator spaces. Functional Analysis [math.FA]. Université Pierre et Marie Curie - Paris VI, 2012. English. ⟨tel-00794951⟩

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