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Berezin Number Inequalities via Convex Functions
by
Huban, Mualla Birgül
, Başaran, Hamdullah
, Gürdal, Mehmet
2022
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Berezin Number Inequalities via Convex Functions
by
Huban, Mualla Birgül
, Başaran, Hamdullah
, Gürdal, Mehmet
2022
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Journal Article
Berezin Number Inequalities via Convex Functions
2022
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Overview
The Berezin symbol à of an operator A on the reproducing kernel Hilbert space 𝓗(Ω) over some set Ω with the reproducing kernel kξ
is defined by
A
˜
(
ξ
)
=
〈
A
k
ξ
‖
k
ξ
‖
,
k
ξ
‖
k
ξ
‖
〉
,
ξ
∈
Ω
. The Berezin number of an operator A is defined by
ber
(
A
)
:
=
sup
ξ
∈
Ω
|
A
˜
(
ξ
)
|
. We study some problems of operator theory by using this bounded function Ã, including treatments of inner product inequalities via convex functions for the Berezin numbers of some operators. We also establish some inequalities involving of the Berezin inequalities.
Publisher
University of Nis, Faculty of Sciences and Mathematics
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