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 Title: Operators and subspaces of L(,0) Author(s): Faber, Richard George Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics 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 $L\sb0$. Issue Date: 1995 Type: Text Language: English URI: http://hdl.handle.net/2142/19751 Rights Information: Copyright 1995 Faber, Richard George Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9601091 OCLC Identifier: (UMI)AAI9601091
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