relation: http://acta.bibl.u-szeged.hu/55800/
title: Preservers of isometries
creator:  Ilišević Dijana
creator:  Kuzma Bojan
creator:  Li Chi-Kwong
creator:  Poon Edward
description: Let γ be a unimodular complex number, and let k be an integer. Then γAk is an isometry for any isometry A of a complex Banach space. It is shown that if f is an analytic function on the unit circle sending an isometry to an isometry for any norm, then f has the form z 7→ γzk for some unimodular γ and integer k. The same conclusion on f can be deduced if f is merely continuous and preserves the isometries of some special classes of norms on a fixed finite-dimensional complex Banach space. The result is extended to real Banach spaces X with dim X ≥ 4, and it is shown that one cannot get the same conclusion on f if dim X < 4. Further extensions of these results are also considered.
date: 2018
type: Cikk, tanulmány, mű
type: NonPeerReviewed
format: part
language: hu
identifier: http://acta.bibl.u-szeged.hu/55800/1/math_084_numb_001-002_003-017.pdf
identifier:    Ilišević Dijana;  Kuzma Bojan;  Li Chi-Kwong;  Poon Edward:   Preservers of isometries.  In: Acta scientiarum mathematicarum, (84) 1-2.  pp. 3-17. (2018)   
relation: http://www.acta.hu