Optimization and differentiation in Banach spaces
type: Item
instance of: scholarly article
title: Optimization and differentiation in Banach spaces
zbMATH Open document ID: 0633.46042
DOI: 10.1016/0024-3795(86)90314-9
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: The author shows that some old ideas of Smulian can be used to give another proof of a theorem of Bourgain which characterizes RNP sets in terms of strongly exposed points. By means of optimization results, he gives a characterization theorem on RNP sets in real Banach spaces with a more concise proof than before. This theorem also shows that a converse of the main result in his earlier paper [Math. Ann. 236, 171-176 (1978; Zbl 0365.49006)] holds. Furthermore, some attempts to extend optimization results obtained in real Banach spaces to the case of complex ones have been made.
reviewed by: Minoru Matsuda
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 46B22
Mathematics Subject Classification ID: 49J27
zbMATH DE Number: 4030249
zbMATH Keywords: Radon-Nikodym property
zbMATH Keywords: strongly exposed points
author: Charles P. Stegall
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90314-9
OpenAlex ID: W2018970665
cites work: Q3256687
cites work: Strongly Exposed Points in Weakly Compact Convex Sets in Banach Spaces
cites work: On dentability and the Bishop-Phelps property
cites work: Geometric aspects of convex sets with the Radon-Nikodym property
cites work: Hamilton-Jacobi equations in infinite dimensions. I: Uniqueness of viscosity solutions
cites work: Hamilton-Jacobi equations in infinite dimensions. II: Existence of viscosity solutions
cites work: Differentiable Functions and Rough Norms on Banach Spaces
cites work: Optimization of functions on certain subsets of Banach spaces
cites work: The Radon-Nikodym Property in Conjugate Banach Spaces. II
cites work: The duality between Asplund spaces and spaces with the Radon-Nikodym property
cites work: Q3756773
description: scientific article; zbMATH DE number 4030249