Operator inequalities in reproducing kernel Hilbert spaces
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Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi
Abstract
In this paper, by using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for the Berezin number
b
e
r
(
A
)
for some self-adjoint operators
A
on
H
(
Ω
)
. Namely, some Mulholland type inequality for reproducing kernel Hilbert space operators are established. By applying this inequality, we prove that
(
b
e
r
(
A
)
)
n
≤
C
1
b
e
r
(
A
n
)
for any positive operator
A
on
H
(
Ω
)
.
Description
Keywords
Mulholland type inequality, Berezin number, positive operator, reproducing kernel Hilbert space, Berezin symbol