Sentence examples for operator connection from inspiring English sources

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 section, we give various characterizations for the non-regularity of an operator connection.

Given an operator connection σ, there is a unique operator monotone function (f:[0,infty) to[0,infty)) such that f(A) = I mathbin {sigma }A, quad A geqslant 0. (5.4) In fact, the map (sigmamapsto f) is a bijection. In addition, σ is a mean if and only if (f(1)=1). Such a function f is called the representing function of σ.

We investigate the regularity of operator connections in Section 4.

We generalize this concept to operator means or, more generally, operator connections as follows.

In Section 2, the concept of cancellability of operator connections is defined and characterized.

In the present paper, we introduce the concept of cancellability for operator connections in a natural way.

It was shown in [12] that there is a one-to-one correspondence between operator connections and monotone metrics.

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.

operator connections on (B(mathbb {H})^); operator monotone functions from (mathbb {R}^) to (mathbb {R}^); finite (positive) Borel measures on ([0,1]); monotone (Riemannian) metrics on the smooth manifold of positive definite matrices.