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

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Adv. Fixed Point Theory 11 (2021), Article ID 19

The phase-isometries between the unit sphere of lp(Γ,H)-type spaces

Meimei Song, Jinshang Du

PDF (136.3 KB) https://doi.org/10.28919/afpt/6780

Abstract

In this paper, Suppose that f: SX → SY is a surjective phase-isometry between the unit spheres of two real lp(Γ,H)-type spaces X and Y. We prove that the mapping f is phase equivalent to an isometry. Otherwise, this isometry is the restriction of a linear isometry between the whole spaces, i.e., this isometry on the unit sphere can be linearly extended into isometry in the whole space.

Published
26 November 2021
Volume
11 (2021)
License
CC BY 3.0

Copyright © 2021 Meimei Song, Jinshang Du. 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. Song, J. Du, The phase-isometries between the unit sphere of lp(Γ,H)-type spaces, Adv. Fixed Point Theory 11 (2021), 19. https://doi.org/10.28919/afpt/6780

BibTeX
@article{Song2021,
  author  = {Song, Meimei and Du, Jinshang},
  title   = {The phase-isometries between the unit sphere of lp(Γ,H)-type spaces},
  journal = {Adv. Fixed Point Theory},
  volume  = {11},
  year    = {2021},
  pages   = {19},
  doi     = {10.28919/afpt/6780}
}