%N 1-2
%K Izometria
%D 2018
%O Bibliogr.: p. 16-17. ; Összefoglalás angol nyelven
%V 84
%L acta55800
%P 3-17
%X 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.
%A  Ilišević Dijana
%A  Kuzma Bojan
%A  Li Chi-Kwong
%A  Poon Edward
%T Preservers of isometries
%J Acta scientiarum mathematicarum