Today at the institute seminar prof. of Kral Saud University Mubariz Tapdiq oglu Garayev gave a talk on “Some applications of generating kernels, English algebras”. English Algebras known well in operator theory was first determined and studied in 1995 by English.
In the talk, using generating kernel and Berezin symbol notion, to English algebras was given a new definition. Using the technique of the Berezin symbol, some new results on algebras are obtained. These results allow to respond to some issues arising in different fields of operators theory. Application of the obtained result to Riccati’s operator, to becoming zero of the product and to invariant subspace problems of operators is given.

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