Buzano, Kreĭn and Cauchy-Schwarz inequalities

Mohammad Sababheh, Hamid Reza Moradi, Zahra Heydarbeygi

Published 2020-10-06Version 1

The Cauchy-Schwarz, Buzano and Kre\u{i}n inequalities are three inequalities about inner product. The main goal of this article is to present refinements of Buzano and Cauchy-Schwarz inequalities, and to present a new proof of a refined version of a Kre\u{i}n-type inequality. Applications that include Buzano-type inequalities for contractions, operator norm and numerical radius inequalities of Hilbert space operators will be presented.