COSINE FAMILIES OF OPERATORS HAVE THE SVEP

Abstract

Let (C(t))_t∈R be a strongly continuous cosine function of opera-
tors on a Banach space X with infinitesimal generator A. In this paper, we
prouve that A has the SVEP if and only if C(t) has the SVEP for all t ∈ R if
and only if C(t_0) has the SVEP for some t_0 ∈ R.