Infinite-Dimensional Diagonalization

Abstract

Let V be an arbitrary vector space over a field K, and let End(V) be the ring of all K-linear transformations of V. We characterize the diagonalizable linear transformations in End(V), as well as the (simultaneously) diagonalizable subalgebras of End(V), generalizing results from classical finite-dimensional linear algebra.These characterizations are formulated in terms of a natural topology on End(V), which reduces to the discrete topology when V is finite-dimensional. This work was done jointly with Miodrag Iovanov and Manuel Reyes.