The structure of the norned lattice generated by the closed bounded convex subsets of a normed space

Title: The structure of the norned lattice generated by the closed bounded convex subsets of a normed space
Creator: Bendit, Theo; Sims, Brailey
Relation: Journal of Nonlinear and Convex Analysis Vol. 17, Issue 6, p. 1069-1081
Relation: http://www.ybook.co.jp/online2/jncav17-6.html
Publisher: Yokohama Publishers
Resource Type: journal article
Date: 2016
Description: Let C(X) denote the set of all non-empty closed bounded convex subsets of a normed linear space X. In 1952 Hans Rådström described how C(X) equipped with the Hausdorff metric could be isometrically embedded in a normed lattice with the order an extension of set inclusion. We call this lattice the Rådström of X and denote it by R(X). We: (1) outline Rådström's construction, (2) examine the structure and properties of R(X) as a Banach space, including; completeness, density character, induced mappings, inherited subspace structure, reflexivity, and its dual space, and (3) explore possible synergies with metric fixed point theory.
Subject: normed linear space; family of closed bounded convex sets; kakutani space; normed linear lattice; fixed point theory; set mappings; Rådström construction
Identifier: http://hdl.handle.net/1959.13/1343491
Identifier: uon:29184
Identifier: ISSN:1880-5221
Language: eng
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