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BUZANO’S INEQUALITY HOLDS FOR ANY PROJECTION
Part of
- Inequalities
- Normed linear spaces and Banach spaces; Banach lattices
S. S. DRAGOMIR
Journal:

Bulletin of the Australian Mathematical Society / Volume 93 / Issue 3 / June 2016

Published online by Cambridge University Press:

20 January 2016, pp. 504-510

Print publication:

June 2016
- Article
- - You have access
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We show that, in an inner product space $H$, the inequality
$$\begin{eqnarray}{\textstyle \frac{1}{2}}[\Vert x\Vert \,\Vert y\Vert +|\langle x,y\rangle |]\geq |\langle Px,y\rangle |\end{eqnarray}$$
is true for any vectors $x,y$ and a projection $P:H\rightarrow H$. Applications to norm and numerical radius inequalities of two bounded operators are given.