Approximate spectral cosynthesis in the harmonically weighted Dirichlet spaces

Yilmaz F.

Hacettepe Journal of Mathematics and Statistics, vol.52, no.3, pp.721-728, 2023 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.15672/hujms.1171901
  • Journal Name: Hacettepe Journal of Mathematics and Statistics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.721-728
  • Keywords: invariant subspaces, weighted Dirichlet spaces
  • Ankara Yıldırım Beyazıt University Affiliated: No

Abstract

For a finite positive Borel measure µ on the unit circle, let D(µ) be the associated harmonically weighted Dirichlet space. A shift invariant subspace M recognizes strong approximate spectral cosynthesis if there exists a sequence of shift invariant subspaces Mk, with finite codimension, such that the orthogonal projections onto Mk converge in the strong operator topology to the orthogonal projection onto M. If µ is a finite sum of atoms, then we show that shift invariant subspaces of D(µ) admit strong approximate spectral cosynthesis.