Proving and Extending Greub-Reinboldt Inequality Using the Two Nonzero Component Lemma

Abstract

We will use the author's Two Nonzero Component Lemma to give a new proof for the GreubReinboldt Inequality. This method has the advantage of showing exactly when the inequality becomes equality. It also provides information about vectors for which the inequality becomes equality. Furthermore, using the Two Nonzero Component Lemma, we will generalize GreubReinboldt Inequality to operators on infinite dimensional separable Hilbert spaces.