Bounded Operators on Topological Vector Spaces and Their Spectral Radii

Shirin Hejazian, Madjid Mirzavaziri, Omid Zabeti

We consider three classes of bounded linear operators on a topological vector space with respect to three different topologies which are introduced by Troitsky. We obtain some properties for the spectral radii of a linear operator on a topological vector space. We find some sufficient conditions for the completeness of these classes of operators. Finally, as a special application, we deduce some sufficient conditions for invertibility of a bounded linear operator.