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


Koca-Eskisehirli B. B.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, cilt.48, sa.6, ss.3047-3057, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 6
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s41980-022-00685-0
  • Dergi Adı: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH
  • Sayfa Sayıları: ss.3047-3057
  • Anahtar Kelimeler: Hardy space, Invariant subspace, Resolvent estimate, Toeplitz operator
  • İstanbul Üniversitesi Adresli: Evet

Özet

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.