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Diametral dimension and property Omega Bar for spaces Snu

By Loïc Demeulenaere


Spaces Snu are metrizable sequence spaces defined by Jaffard in the context of multifractal analysis and signal treatment. From a functional analysis point of view, the study of these spaces points out some topological properties, such as the facts they are locally pseudoconvex in general and locally p-convex in certain cases, Schwartz, and non-nuclear. In this talk, we focus on two topological invariants, namely the diametral dimension (Bessaga, Mityagin, Pelczynski, Rolewicz) and the property "Omega Bar" (Vogt, Wagner). Firstly, we revisit a result of Aubry and Bastin giving the diametral dimension of locally p-convex spaces Snu and extend it to some non-locally p-convex spaces Snu. Secondly, we explain how these developments can be used to prove that a subclass of spaces Snu (among which the locally p-convex ones) verifes the condition Omega Bar

Topics: Diametral dimension, Property Omega Bar, Spaces Snu, Physical, chemical, mathematical & earth Sciences :: Mathematics, Physique, chimie, mathématiques & sciences de la terre :: Mathématiques
Year: 2017
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