Abstract
An operator connection is a binary operation assigned to each pair of positive operators satisfying monotonicity, continuity from above, and the transformer inequality. A normalized operator connection is called an operator mean. In this paper, we introduce and characterize the concepts of cancellability and regularity of operator connections with respect to operator monotone functions, Borel measures, and certain nonlinear operator equations. As applications, we investigate the existence and the uniqueness of solutions for operator equations involving various kind of operator means.
Highlights
1 Introduction A general theory of connections and means for positive operators was given by Kubo and Ando [ ]
A connection σ on B(H)+ can be characterized via operator monotone functions as follows
We introduce the concept of cancellability for operator connections in a natural way
Summary
A general theory of connections and means for positive operators was given by Kubo and Ando [ ]. A connection σ on B(H)+ can be characterized via operator monotone functions as follows.
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