Berezin Number and Numerical Radius Inequalities
Vietnam Journal of Mathematics - Trang 1-13 - 2023
Tóm tắt
We present several inequalities of the Berezin norm and Berezin number for reproducing kernel Hilbert space operators which improve the existing bounds. Among these inequalities, it is shown that if A be a bounded linear operator on a reproducing kernel Hilbert space, then
$$ {\textbf {ber}}^2(A) \le \frac{1}{4}{\textbf {ber}}^2(|A|+i|A^*|)+\frac{1}{8}\Vert |A|+|A^*|\Vert ^2_{\text {ber}}, $$
where
$${\textbf {ber}}(A)$$
and
$$\Vert A\Vert _{\text {ber}}$$
are the Berezin number and Berezin norm of A, respectively. Furthermore, we obtain upper bounds of operator norm and numerical radius for the sum of two operators on a complex Hilbert space.
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