A Note on Convergence Fields
I. D. Berg · Canadian Journal of Mathematics · 1966
The purpose of this note is to show that the (bounded) convergence field of a conservative matrix is closed under a certain diagonalization procedure. As an application of the above result we establish a conjecture of Hill and Sledd in (1) and obtain a result of Lorentz originally proved in (2). First we introduce some notation and definitions, most of which are standard. Let l∞ denote the Banach space of bounded sequences with the supremum norm and let c denote the closed subspace of l∞ consisting of convergent sequences.