Yang, Bicheng On the norm of a self-adjoint operator and applications to the Hilbert’s type inequalities. (English) Zbl 1128.47010 Bull. Belg. Math. Soc. - Simon Stevin 13, No. 4, 577-584 (2006). The author investigates a new bilinear inequality with a best constant factor and studies some new Hilbert type inequalities by using the Cauchy–Schwarz inequality and the inequality \[ | \langle a, Tb\rangle| \leq \frac{\| T\| }{\sqrt{2}} \left(\| a\| ^2\| b\| ^2 + \langle a, b\rangle^2\right)^{1/2}, \] where \(a, b\) are in a real separable Hilbert space \(H\) and \(T\) is a semi-definite bounded operator; cf.Z.Kewei [J. Math.Anal.Appl.271, No.1, 288–296 (2002; Zbl 1016.15015)]. Reviewer: Mohammad Sal Moslehian (Mashhad) Cited in 1 ReviewCited in 7 Documents MSC: 47A30 Norms (inequalities, more than one norm, etc.) of linear operators 26D15 Inequalities for sums, series and integrals 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) Keywords:norm; selfadjointness; bilinear inequality; Hilbert type inequality; beta function Citations:Zbl 1016.15015 PDFBibTeX XMLCite \textit{B. Yang}, Bull. Belg. Math. Soc. - Simon Stevin 13, No. 4, 577--584 (2006; Zbl 1128.47010)