Generally unbounded infinitesimal generators are studied in the context of operator topology. Beginning with the definition of seminorm, the concept of locally convex topological vector space is introduced as well as the concept of Fréchet space. These are the basis for defining operator topologies. Consequently, by associating the topological properties with the convergence of sequence, a suitable mathematical framework for obtaining the logarithmic representation of infinitesimal generators is presented.
Part of the book: Structure Topology and Symplectic Geometry