  In this paper we present some spectral property for quotient bounded
operators and locally bounded operators on locally convex spaces. We introduce
the spectral radius of a quotient bounded operator and we show that the Gelfand
formula for spectral radius and Newmann series have the same properties like in
Banach spaces. Moreover, the geometrical radius of the spectrum is equal with
the spectral radius. Using definitions of V.Troitsky we prove that the spectral
set of a quotient bounded operator is compact set.
