We will use the author’s Two Nonzero Component Lemma to give a new proof for the Greub-Reinboldt Inequality. This method has the advantage of showing exactly when the inequality becomes equality. It also provides inf...We will use the author’s Two Nonzero Component Lemma to give a new proof for the Greub-Reinboldt 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 Greub-Reinboldt Inequality to operators on infinite dimensional separable Hilbert spaces.展开更多
文摘We will use the author’s Two Nonzero Component Lemma to give a new proof for the Greub-Reinboldt 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 Greub-Reinboldt Inequality to operators on infinite dimensional separable Hilbert spaces.
