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Faber, Richard George 2011-05-07T12:17:21Z 2011-05-07T12:17:21Z 10000-01-01 1995 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 $L\sb0$. Made available in DSpace on 2011-05-07T12:17:21Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9601091.pdf: 1142157 bytes, checksum: 77593d74e615ac66c470f8385d43f53c (MD5) Previous issue date: 1995 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:39:11Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:16:27-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9601091 (UMI)AAI9601091 http://hdl.handle.net/2142/19751 eng Copyright 1995 Faber, Richard George Mathematics Operators and subspaces of L(,0) text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.