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BUZANO’S INEQUALITY HOLDS FOR ANY PROJECTION
- Part of
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- 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
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- Article
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We show that, in an inner product space
$H$, the inequality is true for any vectors
$$\begin{eqnarray}{\textstyle \frac{1}{2}}[\Vert x\Vert \,\Vert y\Vert +|\langle x,y\rangle |]\geq |\langle Px,y\rangle |\end{eqnarray}$$
$x,y$ and a projection 
$P:H\rightarrow H$. Applications to norm and numerical radius inequalities of two bounded operators are given.
QUASILINEARITY OF SOME COMPOSITE FUNCTIONALS WITH APPLICATIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 83 / Issue 1 / February 2011
- Published online by Cambridge University Press:
- 17 September 2010, pp. 108-121
- Print publication:
- February 2011
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- Article
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- You have access
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