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https://hdl.handle.net/2142/19751
Description
Title
Operators and subspaces of L(,0)
Author(s)
Faber, Richard George
Issue Date
1995
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
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 $L\sb0$.
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