On Some Generalizations of Cauchy–Schwarz Inequalities and Their Applications
Najla Altwaijry, Kais Feki, Nicuşor Minculete
Abstract
The aim of this paper is to provide new upper bounds of ω(T), which denotes the numerical radius of a bounded operator T on a Hilbert space (H,⟨·,·⟩). We show the Aczél inequality in terms of the operator |T|. Next, we give certain inequalities about the A-numerical radius ωA(T) and the A-operator seminorm ∥T∥A of an operator T. We also present several results related to the A-numerical radius of 2×2 block matrices of semi-Hilbert space operators, by using symmetric 2×2 block matrices.
Topics & Concepts
MathematicsOperator matrixHilbert spaceOperator (biology)Bounded functionCauchy–Schwarz inequalityRADIUSPure mathematicsBounded operatorMathematical analysisInequalityComputer scienceComputer securityTranscription factorGeneChemistryRepressorBiochemistryMathematical Inequalities and ApplicationsMatrix Theory and AlgorithmsHolomorphic and Operator Theory