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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8385-4-2016,
author = {Mubariz T. Karaev and Mehmet G\"urdal and Mualla Birg\"ul Huban},
title = {Reproducing kernels, Engli\v s algebras and some applications},
journal = {Studia Mathematica},
volume = {233},
year = {2016},
pages = {113-141},
zbl = {06575026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8385-4-2016}
}
Mubariz T. Karaev; Mehmet Gürdal; Mualla Birgül Huban. Reproducing kernels, Engliš algebras and some applications. Studia Mathematica, Tome 233 (2016) pp. 113-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8385-4-2016/