Spectral Properties of Two Classes of Toeplitz Operators on H-p, 1 < p < infinity

Koca-Eskisehirli B. B.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol.48, no.6, pp.3047-3057, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.1007/s41980-022-00685-0
  • Journal Name: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH
  • Page Numbers: pp.3047-3057
  • Keywords: Hardy space, Invariant subspace, Resolvent estimate, Toeplitz operator
  • Istanbul University Affiliated: Yes

Abstract

In this study, we consider two classes of Toeplitz operators on H-p, 1 < p < infinity: Toeplitz operators with unimodular symbols and Toeplitz operators whose spectra satisfy a specific geometric condition (the circular convexity condition). We give some inclusions for their spectrum and some estimates for their resolvents. Using obtained results, we show the existence of nontrivial invariant subspaces of these types of Toeplitz operators. This result gives a partially answer to the question of which type operators on a Banach space has a nontrivial invariant subspace.