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Advances in Fixed Point Theory ISSN 1927-6303 (Print)

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Adv. Fixed Point Theory 13 (2023), Article ID 14

The Tingley problem on the unit sphere of complex Lp[0,1] space

Meixuan Lv

PDF (186.4 KB) https://doi.org/10.28919/afpt/8133

Abstract

In this paper, we investigate the problem of extending isometric operators from unit sphere of complex Lp spaces (1<p<∞, p≠2) to general complex Banach spaces. By studying the isometric operators, we prove the Tingley problem on complex Lp spaces and provide a positive answer under some conditions. That is, it is proved that for a surjective isometry V0 on any complex Lp[0,1] unit sphere to any general complex Banach space E unit sphere, Under some conditions,V0 can be extended to a linear isometry from the entire space Lp[0,1] to E.

Published
18 September 2023
Volume
13 (2023)
License
CC BY 3.0

Copyright © 2023 Meixuan Lv. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

M. Lv, The Tingley problem on the unit sphere of complex Lp[0,1] space, Adv. Fixed Point Theory 13 (2023), 14. https://doi.org/10.28919/afpt/8133

BibTeX
@article{Lv2023,
  author  = {Lv, Meixuan},
  title   = {The Tingley problem on the unit sphere of complex Lp[0,1] space},
  journal = {Adv. Fixed Point Theory},
  volume  = {13},
  year    = {2023},
  pages   = {14},
  doi     = {10.28919/afpt/8133}
}