Tapdıgoğlu, Ramiz
(2021)
*New berezin symbol inequalities for operators on the reproducing kernel hilbert space.*
Operators and Matrices, 15
(3).
pp. 1031-1043.
ISSN 1846-3886

Official URL: https://dx.doi.org/10.7153/oam-2021-15-64

## Abstract

We use Kittaneh and Manasrah inequality and Kian’s functional calculus method to prove some new inequalities for Berezin symbols and Berezin numbers of operators. In particular, we prove that ( ber f (A)2) (f(A) p ≥ ber +f )(A)q p q for all self-adjoint operators A on the reproducing kernel Hilbert space H (Ω) with spectrum in J ⊂ (−∞,+∞) and all continuous nonnegative functions f defined on J. We also prove new upper and lower bounds for Berezin numbers of reproducing kernel Hilbert space operators. Among our results, we prove that if A: H (Ω) → H (Ω) is a bounded pseudo-hypornormal operator on the reproducing kernel Hilbert space H (Ω), then for all non-negative non-decreasing pseudo-operator convex function f on [0,∞), we have ⎛ ⎞ ⎛ ⎞ f (ber(A)) ≥12 ∥f ⎝|A| ⎠ + f ⎝|A∗ | ⎠ 1 +ξ|A|2 8 1 +ξ|A|2, ∥ 8 Ber where ‖.‖Ber denotes the Berezin norm of operator.

Item Type: | Article |
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Uncontrolled Keywords: | Berezin norm; Berezin number; Berezin symbol; Functional calculus; Reproducing kernel Hilbert space; Self-adjoint operator |

Divisions: | Faculty of Engineering and Natural Sciences |

Depositing User: | Ramiz Tapdıgoğlu |

Date Deposited: | 28 Aug 2022 16:07 |

Last Modified: | 28 Aug 2022 16:07 |

URI: | https://research.sabanciuniv.edu/id/eprint/43803 |