Abstract. In this paper we provide a new proof of the operator version of Julia's lemma which was proven by Ky Fan in [fan6]. The advantage of our method is that we can actually improve the inequality [fan6, p. 242 (a)].

DOI: 10.14232/actasm-014-076-6

AMS Subject Classification (1991): 47A63

Keyword(s): positive operators, strictly positive operators

Received November 20, 2014, and in final form February 24, 2015. (Registered under 76/2014.)