On Wigner's theorem in strictly convex normed spaces

2020 ◽  
Vol 97 (3-4) ◽  
pp. 393-401 ◽  
Author(s):  
Dijana Ilisevic ◽  
Aleksej Turnsek
Keyword(s):  
Normed Spaces ◽  
Strictly Convex ◽  
Wigner’S Theorem ◽  
Wigner's Theorem

On maps that preserve orthogonality in normed spaces

2006 ◽  
Vol 136 (4) ◽  
pp. 709-716 ◽  
Author(s):  
A. Blanco ◽  
A. Turnšek
Keyword(s):  
Banach Spaces ◽  
Wide Class ◽  
Normed Spaces ◽  
Linear Map ◽  
Wigner’S Theorem ◽  
Scalar Multiple ◽  
Symmetry Transformations ◽  
Orthogonality In Normed Spaces ◽  
Wigner's Theorem

We show that every orthogonality-preserving linear map between normed spaces is a scalar multiple of an isometry. Using this result, we generalize Uhlhorn's version of Wigner's theorem on symmetry transformations to a wide class of Banach spaces.

scholarly journals On Wigner’s theorem in smooth normed spaces

2020 ◽  
Vol 94 (6) ◽  
pp. 1257-1267
Author(s):  
Dijana Ilišević ◽  
Aleksej Turnšek
Keyword(s):  
Normed Spaces ◽  
Wigner’S Theorem ◽  
Wigner's Theorem

A Variant of Wigner’s Theorem in Normed Spaces

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Dijana Ilišević ◽  
Aleksej Turnšek
Keyword(s):  
Normed Spaces ◽  
Wigner’S Theorem ◽  
Wigner's Theorem

scholarly journals On the Aleksandrov-Rassias Problems on Linearn-Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yumei Ma
Keyword(s):  
Normed Spaces ◽  
Unit Distance ◽  
Strictly Convex ◽  
Surjective Mapping

This paper generalizes T. M. Rassias' results in 1993 ton-normed spaces. IfXandYare two realn-normed spaces andYisn-strictly convex, a surjective mappingf:X→Ypreserving unit distance in both directions and preserving any integer distance is ann-isometry.

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