Some Upper Bounds For The Berezin Number of Hilbert Space Operators
Abstract
In this paper, we obtain some Berezin number inequalities
based on the definition of Berezin symbol. Among other inequalities,
we show that if A;B be positive definite operators in B(H), and A♯B
is the geometric mean of them, then
ber2(A♯B) ber
(
A2 + B2
2
)
???? 1
2
inf
2Ω
(^k);
where (^k) = ⟨(A ???? B)^k; ^k⟩2; and ^k is the normalized reproducing
kernel of the space H for belong to some set Ω:
based on the definition of Berezin symbol. Among other inequalities,
we show that if A;B be positive definite operators in B(H), and A♯B
is the geometric mean of them, then
ber2(A♯B) ber
(
A2 + B2
2
)
???? 1
2
inf
2Ω
(^k);
where (^k) = ⟨(A ???? B)^k; ^k⟩2; and ^k is the normalized reproducing
kernel of the space H for belong to some set Ω:
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