Reproducing kernels, Engliš algebras and some applications

Karaev M. T., GÜRDAL M., HUBAN M. B.

Studia Mathematica, cilt.232, sa.2, ss.113-141, 2016 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 232 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.4064/sm8385-4-2016
  • Dergi Adı: Studia Mathematica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.113-141
  • Anahtar Kelimeler: Berezin symbol, Hardy space, Invariant subspace, Reproducing kernel, Riccati equation, Toeplitz operator
  • Isparta Uygulamalı Bilimler Üniversitesi Adresli: Evet

Özet

We introduce the notion of Engliš algebras, defined in terms of reproducing kernels and Berezin symbols. Such algebras were apparently first investigated by Engliš (1995). Here we give some new results on Engliš C∗-algebras on abstract reproducing kernel Hilbert spaces and some applications to various questions of operator theory. In particular, we give applications to Riccati operator equations, zero Toeplitz products, and the existence of invariant subspaces for some operators.