A Novel Proof of Non-supercyclicity of Isometries on Banach Space

Authors

1 Department of Mathematics, College of Sciences, Yasouj University, Yasouj-, Ira

2 Department of Mathematics, College of Sciences, Yasouj University, Yasouj-, Iran

Abstract

As an alternative to the proof given by Ansari and Bourdon [1], we present here a simple and self-contained proof that isometries are not supercyclic. As compared to their proof, which is based on a result that suggests that isometries always have nontrivial invariant subspaces [6], our proof is independent of this result and provides a more direct proof that isometries do not have supercyclic vectors.

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History

  • Receive Date: 15 August 2024
  • Revise Date: 04 December 2024
  • Accept Date: 22 December 2024

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