This is an announcement for the paper "Generalized Jacobian for functions with infinite dimensional range and domain" by Zsolt P'ales and Vera Zeidan.
Abstract: In this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon--Nikod'ym property, Clarke's generalized Jacobian will be extended to this setting. Characterization and fundamental properties of the extended generalized Jacobian are established including the nonemptiness, the $\beta$-compactness, the $\beta$-upper semicontinuity, and a mean-value theorem. A connection with known notions is provided and chain rules are proved using key results developed. This included the vectorization and restriction theorem, and the extension theorem. Therefore, the generalized Jacobian introduced in this paper is proved to enjoy all the properties required of a derivative like-set.
Archive classification: Functional Analysis
Mathematics Subject Classification: 49J52
The source file(s), gen-jacobian3a.tex: 25440 bytes, is(are) stored in gzipped form as 0605771.gz with size 9kb. The corresponding postcript file has gzipped size 39kb.
Submitted from: zeidan@math.msu.edu
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