论文标题
广义的buzano不平等
Generalized Buzano Inequality
论文作者
论文摘要
If $P$ is an orthogonal projection defined on an inner product space $\mathcal{H}$, then the inequality $$ |\langle Px, y\rangle|\leq \frac12 [\|x\|\|y\|+|\langle x, y\rangle|] $$ fulfills for any $x,y \in \ Mathcal {h} $（请参阅\ cite {dra16}）。特别是，当$ p $是身份操作员时，它会恢复著名的Buzano不平等现象。我们获得了这种经典不平等的概括，这些不平等适用于在$ \ Mathcal {H} $上定义的某些有限线性操作员的家庭。此外，还建立了涉及运算符规范和数值半径的几种新的不平等现象。
If $P$ is an orthogonal projection defined on an inner product space $\mathcal{H}$, then the inequality $$ |\langle Px, y\rangle|\leq \frac12 [\|x\|\|y\|+|\langle x, y\rangle|] $$ fulfills for any $x,y \in \mathcal{H}$ (see \cite{Dra16}). In particular, when $P$ is the identity operator, then it recovers the famous Buzano inequality. We obtain generalizations of such classical inequality, which hold for certain families of bounded linear operators defined on $\mathcal{H}$. In addition, several new inequalities involving the norm and numerical radius of an operator are established.
