Some New Applications of Berezin Symbols


Bhunia P., Garayev M. T., Paul K., Tapdigoglu R.

COMPLEX ANALYSIS AND OPERATOR THEORY, vol.17, no.6, 2023 (SCI-Expanded) identifier identifier

Qısa məlumat

We study some problems of operator theory by using Berezin symbols approach. Namely, we investigate in terms of Berezin symbols invariant subspaces of isometric composition operators on H (Omega). We discuss operator corona problem, in particular, the Toeplitz corona problem. Further, we characterize unitary operators in terms of Berezin symbols. We show that the well known inequality w (A) >= 1/2 parallel to A parallel to for numerical radius is not true for the Berezin number of operators, which is defined) by ber (A) := sup(lambda is an element of Omega) vertical bar(a) over tilde(lambda)vertical bar where (A) over tilde (lambda) := < A (k) over tilde (lambda,) k(lambda)> is the Berezin symbol of operator A : H (Omega) -> H (Omega). Finally, we provide a lower bound for ber (A) .