Some applications of Schwarz lemma for operators (Q1826086)

Let A be a bounded linear operator on a complex Hilbert space and let f be an analytic function admissible in the Riesz-Dunford functional for A. The author claims to have obtained a generalized Schwarz lemma and some Harnack type inequalities for operators of type f(A). However the paper is badly written and the function \(f(z)=z^ 2\) is a counterexample for the current version of theorem 1. Related results can be found in papers by \textit{Ky Fan} [Math. Z. 160, 275-290 (1978; Zbl 0455.47013) and Math. Z. 179, 293-298 (1982; Zbl 0465.47017)].