Original title: Separable reductions and rich families in theory of Fréchet subdifferentials
Authors: Fabian, Marián
Document type: Papers
Conference/Event: Spring School on Variational Analysis 2015, Paseky nad Jizerou (CZ), 20150419
Year: 2015
Language: eng
Abstract: We consider important properties of Fréchet subdifferentials, in particular: the non-emptiness of subdifferentials, the non-zeroness of normal cones, the fuzzy calculus, and the extremal principle; all statements being considered in Fréchet sense. Given a nonseparable Banach space X, we show how the validity of these statements is implied by the validity of them in every separable subspace of X. Such a reasoning is called “separable reduction”. We show that, behind this approach, there is a modern and powerful concept of rich subfamily of the family of all separable subspaces of X.
Keywords: Fréchet subdifferentials
Project no.: GAP201/12/0290 (CEP)
Funding provider: GA ČR
Host item entry: Variational Analysis and its Applications, ISBN 978-80-7378-288-7

Institution: Institute of Mathematics AS ČR (web)
Document availability information: Fulltext is available on demand via the digital repository of the Academy of Sciences.
Original record: http://hdl.handle.net/11104/0253703

Permalink: http://www.nusl.cz/ntk/nusl-201294


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