A generalization of parallel addition

Summary Parallel addition of positive operators, a concept introduced by W. N. Anderson and R. J. Duffin 1] in connection with network theory, has already been studied by several authors. We specifically mention W. N. Anderson and G. E. Trapp 2] and 3], T. Ando 4], K. Nishio 12], E. L. Pekarev and J. L. Smul'jan 13], as well as the article 10] by the present authors.The purpose of this note is to study a generalization of parallel addition. In particular, it will be shown (Theorem 3.2) that the corresponding quasi-units, a concept introduced in 10], are again the extreme points of the convex sets, formed by the positive operators less than or equal to some fixed operator.