Preservers of isometries

Ilišević, Dijana and Kuzma, Bojan and Li, Chi-Kwong and Poon, Edward: Preservers of isometries. Acta scientiarum mathematicarum, (84) 1-2. pp. 3-17. (2018)

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Abstract

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.

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2018
Volume: 84
Number: 1-2
Page Range: pp. 3-17
ISSN: 0001-6969
Uncontrolled Keywords: Izometria
Additional Information: Bibliogr.: p. 16-17. ; Összefoglalás angol nyelven
Official URL: http://www.acta.hu
Date Deposited: 2018. Nov. 10. 08:20
Last Modified: 2019. Sep. 09. 13:44
URI: http://acta.bibl.u-szeged.hu/id/eprint/55800

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