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Theses
UMD property for Banach spaces and operator spaces
UMD property for Banach spaces and operator spaces
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$.
Cited literature [32 references]
https://tel.archives-ouvertes.fr/tel-00794951
Contributor : Yanqi Qiu <>
Submitted on : Tuesday, February 26, 2013 - 5:06:54 PM
Last modification on : Thursday, December 10, 2020 - 10:54:49 AM
Long-term archiving on: : Sunday, April 2, 2017 - 5:54:09 AM
Contributor : Yanqi Qiu <>
Submitted on : Tuesday, February 26, 2013 - 5:06:54 PM
Last modification on : Thursday, December 10, 2020 - 10:54:49 AM
Long-term archiving on: : Sunday, April 2, 2017 - 5:54:09 AM