Comparison of various means for operators
Let \(A\), \(B\) be nonnegative Hilbert space operators and let \(T\) be an arbitrary linear bounded operator, all acting on a Hilbert space. The inequality \[ \| A^{1/2} TB^{1/2}\|\leq 1/2\| AT+ TB\|, \] was only recently found in operator theory, in connection with some concrete problems of harmonic analysis, see \textit{R. Bhatia} and \textit{C. Davis} [SIAM J. Matrix Annal. Appl. 14, 132-136 (1993; Zbl 0767.15012)]. The note under review contains several interesting refinements and generalizations of this inequality.
scientific article; zbMATH DE number 1286370
scientific article