Greub, W. and Rheinboldt, W. (1959) On a Generalisation of an Inequality of L.V. Kantorovich. Proceedings of the American Mathematical Society, 10, 407-415. http://dx.doi.org/10.1090/S0002-9939-1959-0105028-3

has been cited by the following article:

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

  AUTHORS: Morteza Seddighin

  KEYWORDS: Greub-Reinboldt Inequality, Two Nonzero Component Lemma

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.4 No.2, June 16, 2014

  ABSTRACT: 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.