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arXiv · 2204.14233

Generalized Buzano Inequality

Tamara Bottazzi·Cristian Conde
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Abstract

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.

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Tamara Bottazzi, Cristian Conde. 2022-04-29. Generalized Buzano Inequality. https://arxiv.org/abs/2204.14233

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