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 Society Volume 123, Number 6, June 1995. Copyright 1995 American Mathematical Society. Used by permission.