Concrete Operators (Apr 2022)

Surjective isometries on Banach sequence spaces: A survey

  • Antunes Leandro,
  • Beanland Kevin

DOI
https://doi.org/10.1515/conop-2022-0125
Journal volume & issue
Vol. 9, no. 1
pp. 19 – 40

Abstract

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In this survey, we present several results related to characterizing the surjective isometries on Banach sequence spaces. Our survey includes full proofs of these characterizations for the classical spaces as well as more recent results for combinatorial Banach spaces and Tsirelson-type spaces. Along the way, we pose many open problems related to the structure of the group of surjective isometries for various Banach spaces.

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