## Mathematics, Department of

#### Date of this Version

1995

#### Abstract

Given separable Frechet spaces, E, F , and G , let L(E, F), L(F, G), and L(E, G) denote the space of continuous linear operators from E to F , F to G, and E to G, respectively. We topologize these spaces of operators by any one of a family of topologies including the topology of point-wise convergence and the topology of compact convergence. We will show that if (X, F) is any measurable space and both A: X → L(E, F) and B: X → L(F, G) are Borelian, then the operator composition BA: X → L(E, G) is also Borelian. Further, we will give several consequences of this result.

## Comments

Published in

Proceedings of the American Mathematical SocietyVolume 123, Number 6, June 1995. Copyright 1995 American Mathematical Society. Used by permission.