Reproducing kernels, Engliš algebras and some applications
Volume 232 / 2016
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.
