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Bayoumi quasi-differential is not different from Fréchet-differential

Fernando Albiac, José Ansorena (2012)

Open Mathematics

Unlike for Banach spaces, the differentiability of functions between infinite-dimensional nonlocally convex spaces has not yet been properly studied or understood. In a paper published in this Journal in 2006, Bayoumi claimed to have discovered a new notion of derivative that was more suitable for all F-spaces including the locally convex ones with a wider potential in analysis and applied mathematics than the Fréchet derivative. The aim of this short note is to dispel this misconception, since...

Bounded analytic sets in Banach spaces

Volker Aurich (1986)

Annales de l'institut Fourier

Conditions are given which enable or disable a complex space X to be mapped biholomorphically onto a bounded closed analytic subset of a Banach space. They involve on the one hand the Radon-Nikodym property and on the other hand the completeness of the Caratheodory metric of X .

Capacités gaussiennes

Denis Feyel, A. de La Pradelle (1991)

Annales de l'institut Fourier

On étudie les espaces de Sobolev W r , p ( E , μ ) construits sur un espace localement convexe E muni d’une mesure gaussienne centree μ . Si μ est de Radon, on démontre que les capacités naturelles c r , p sont tendues sur les compacts. Cela résulte d’un principe général relatif aux quasi-normes.On s’intéresse également aux fonctions quasi-continues a valeurs banachiques, ce qui est utile pour les propriétés de Nikodym, et à des applications à la continuité des trajectoires des intégrales stochastiques.

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