On high-power operator inequalities and spectral radii of operators (Q2471372)

The authors prove several power inequalities derived rather directly from the Cauchy--Schwartz inequality. These are used to prove spectral-radius inequalities such as \[ |\langle TSx,Cx\rangle| \leq r(S)\,r(C)\,\langle Tx,x\rangle, \] where the operator \(T\) is positive, \(S\) and \(C\) are operators such that \(TS\) and \(TC\) are selfadjoint.