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BUZANO’S INEQUALITY HOLDS FOR ANY PROJECTION
Published online by Cambridge University Press: 20 January 2016
Abstract
We show that, in an inner product space $H$, the inequality
$$\begin{eqnarray}{\textstyle \frac{1}{2}}[\Vert x\Vert \,\Vert y\Vert +|\langle x,y\rangle |]\geq |\langle Px,y\rangle |\end{eqnarray}$$
$x,y$ and a projection
$P:H\rightarrow H$. Applications to norm and numerical radius inequalities of two bounded operators are given.
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- Research Article
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- © 2016 Australian Mathematical Publishing Association Inc.
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