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Some New Applications of Berezin Symbols

Bhunia, P and Garayev, MT and Paul, K and Tapdigoglu, R (2023) Some New Applications of Berezin Symbols. In: Complex Analysis and Operator Theory, 17 (6).

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Official URL: https://doi.org/10.1007/s11785-023-01404-1


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(Ω). 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)≥12∥A∥ for numerical radius is not true for the Berezin number of operators, which is defined by ber (A) : = sup λ∈Ω| A~ (λ) | , where A~ (λ) : = 〈 Ak^ λ, k^ λ〉 is the Berezin symbol of operator A: H(Ω) → H(Ω). Finally, we provide a lower bound for ber (A). © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Item Type: Journal Article
Publication: Complex Analysis and Operator Theory
Publisher: Birkhauser
Additional Information: The copyright for this article belongs to the Birkhauser.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 07 Nov 2023 05:57
Last Modified: 07 Nov 2023 05:57
URI: https://eprints.iisc.ac.in/id/eprint/83034

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