论文标题
Berezin数字不平等的完整改进
Complete refinements of the Berezin number inequalities
论文作者
论文摘要
在本文中，获得了Berezin数量不平等的几种改进。我们将涉及Berezin编号的功率的不平等现象概括为两个操作员的产品，这些操作员作用于繁殖的内核Hilbert Space $ \ Mathcal H = \ Mathcal H（ω）$，也可以改善它们。除其他不平等外，还表明，如果$ a，b \ in {\ mathcal b}（\ mathcal h）$，以至于$ | a | a | a | b = b = b = b = b = b^{*} | a | $，$ f $和$ f $和$ f $和$ f $和$ f $和$ f $是$ [0，\ infty）$ ge q ge（$ fe）$ f（t）$ f（t） \ begin {align*}＆\ textbf {ber}^{p}（ab）\ leq r^{p}（b）\ times \\＆\ left（\ textbf {ber} \ big（\ frac {1}αf^{αp}（| a |）+\ frac {1}βg^{βp}（| a^{*} |）\ big）\ big）-r_ {0} \ big（\ langle f^{2}（| a |）\ hat {k}_λ，\ hat {k}_λ\ rangle^{αp/4} - \ langle g^{2}（| a^{*} |）\ hat {k}_λ，\ hat {k}_λ\ rangle^{βp/4} \ big） $ \ frac {1}α+\ frac {1}β= 1 $，$βP\ geq2 $和$ r_ {0} = \ min \ {\ frac {1}α，\ frac {1}α，\ frac {1}β\ \} $。
In this paper, several refinements of the Berezin number inequalities are obtained. We generalize inequalities involving powers of the Berezin number for product of two operators acting on a reproducing kernel Hilbert space $\mathcal H=\mathcal H(Ω)$ and also improve them. Among other inequalities, it is shown that if $A,B\in {\mathcal B}(\mathcal H)$ such that $|A|B=B^{*}|A|$, $f$ and $g$ are nonnegative continuous functions on $[0,\infty)$ satisfying $f(t)g(t)=t\,(t\geq 0)$, then \begin{align*} &\textbf{ber}^{p}(AB)\leq r^{p}(B)\times\\&\left(\textbf{ber} \big(\frac{1}αf^{αp}(|A|)+\frac{1}βg^{βp}(|A^{*}|)\big)-r_{0}\big(\langle f^{2}(|A|)\hat{k}_λ,\hat{k}_λ\rangle^{αp/4} -\langle g^{2}(|A^{*}|)\hat{k}_λ,\hat{k}_λ\rangle^{βp/4}\big)^{2}\right) \end{align*} for every $p\geq 1, α\geqβ>1$ with $\frac{1}α+\frac{1}β=1$, $βp\geq2$ and $r_{0}=\min\{\frac{1}α,\frac{1}β\}$.
