Normal decompositions of operator spaces over locally convex spaces (Q1812459)

The main purpose of this paper is to introduce the notion of the so-called ``normal index'' of a linear operator in a locally convex space. This index characterizes the type of continuity of the operator in terms of the corresponding seminorms. The normal decomposition of operator spaces into inductive scales of locally convex spaces in accordance with the classification of operators by their ``normal indices'' is considered, and some canonical isomorphisms of operator spaces over Banach spaces are generalized to operators in locally convex spaces.