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Title:Nearly Representable Operators (dunford-Pettis, Radon-Nikodym)
Author(s):Petrakis, Minos Aristidu
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:In this thesis we introduce the class (DELTA)(X,Y) of nearly represent- able operators from a Banach space X to a Banach space Y. These are the operators that map X-valued uniformly bounded martingales that are Cauchy in the Pettis norm into Y-valued martingales that converge almost everywhere.
We will see that (DELTA)(L('1),X) contains all representable operators and is contained in the class of Dunford-Pettis operators from L('1) to X. We prove that these inclusions are strict in the case X is the space c(,0). We also prove every nearly representable operator from L('1) to a Banach lattice not containing a copy of c(,0) is representable.
We study the class of M(,0)-continuous operators. (An operator T : L('1) (--->) X is called M(,0)-continuous if
(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)
where the supremum is taken over all subintervals I of 0,1 ).
In the last chapter we give geometric conditions on a Banach space X that imply that all operators from L('1) to X are Dunford-Pettis.
Issue Date:1987
Type:Text
Description:93 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987.
URI:http://hdl.handle.net/2142/71251
Other Identifier(s):(UMI)AAI8711851
Date Available in IDEALS:2014-12-16
Date Deposited:1987


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