Generalized Buzano Inequality
Tamara Bottazzi, Cristian Conde

TL;DR
This paper generalizes the classical Buzano inequality to broader classes of bounded linear operators on inner product spaces, and introduces new inequalities related to operator norm and numerical radius.
Contribution
It extends the Buzano inequality to certain families of operators and establishes novel inequalities involving operator norm and numerical radius.
Findings
Generalized Buzano inequalities for specific operator classes
New bounds involving operator norm and numerical radius
Extensions of classical inequalities to broader operator families
Abstract
If is an orthogonal projection defined on an inner product space , then the inequality fulfills for any (see \cite{Dra16}). In particular, when 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 . In addition, several new inequalities involving the norm and numerical radius of an operator are established.
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Taxonomy
TopicsMathematical Inequalities and Applications · Mathematics and Applications · Optimization and Variational Analysis
