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On the Generalizations of the Mazur–Ulam Isometric Theorem

✍ Scribed by Wang Jian

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
112 KB
Volume
263
Category
Article
ISSN
0022-247X

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✦ Synopsis

This paper contains several generalizations of the Mazur-Ulam isometric theorem in F * -spaces which are not assumed to be locally bounded. Let X and Y be two real F * -spaces, and let X be locally pseudoconvex or δ-midpoint bounded. Assume that a operator T maps X onto Y in a δ-locally 1/2 i -isometric manner for all i ∈ 0 ∪ . Then T is affine. In addition, we give the sufficient conditions of a mapping between two topological vector spaces being affine.

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