×

On the norm of a self-adjoint operator and applications to the Hilbert’s type inequalities. (English) Zbl 1128.47010

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)].

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.)

Citations:

Zbl 1016.15015
PDFBibTeX XMLCite