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Reproducing kernels, Engliš algebras and some applications

Volume 232 / 2016

Mubariz T. Karaev, Mehmet Gürdal, Mualla Birgül Huban Studia Mathematica 232 (2016), 113-141 MSC: Primary 47B35. DOI: 10.4064/sm8385-4-2016 Published online: 21 April 2016

Abstract

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 $C^{\ast }$-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.

Authors

  • Mubariz T. KaraevInstitute of Mathematics and Mechanics
    National Academy of Sciences of Azerbaijan
    B. Vagabzade st. 9
    Baku 370141, Azerbaijan
    and
    Department of Mathematics
    College of Science
    King Saud University
    P.O. Box 2455
    Riyadh 11451, Saudi Arabia
    e-mail
  • Mehmet GürdalDepartment of Mathematics
    Suleyman Demirel University
    32260 Isparta, Turkey
    e-mail
  • Mualla Birgül HubanDepartment of Mathematics
    Suleyman Demirel University
    32260 Isparta, Turkey
    e-mail

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