Operators and subspaces of L(,0)

We prove linear and non-linear lifting theorems for locally convex subspaces of $L\sb0,$ and we give a characterization for locally bounded subspaces of $L\sb0.$ For every closed locally convex subspace E of $L\sb0$ and for any continuous linear operator T from $L\sb0$ to $L\sb0/E$ there is a continuous linear operator S from $L\sb0$ to $L\sb0$ such that T = QS where Q is the quotient map from $L\sb0$ to $L\sb0/E$.If X is a paracompact space and E is a closed locally convex subspace the F-space Y then for any continuous map f from X to Y/E there is a continuous map F from X to Y such that F = Qf where Q is the quotient map from Y to Y/E.We give a characterization of locally bounded subspaces of $L\sb0$.U of I OnlyETDs are only available to UIUC Users without author permissio