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Title:  Nearly Representable Operators (dunfordPettis, RadonNikodym) 
Author(s):  Petrakis, Minos Aristidu 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
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 Xvalued uniformly bounded martingales that are Cauchy in the Pettis norm into Yvalued martingales that converge almost everywhere. We will see that (DELTA)(L('1),X) contains all representable operators and is contained in the class of DunfordPettis 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 DunfordPettis. 
Issue Date:  1987 
Type:  Text 
Description:  93 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1987. 
URI:  http://hdl.handle.net/2142/71251 
Other Identifier(s):  (UMI)AAI8711851 
Date Available in IDEALS:  20141216 
Date Deposited:  1987 
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Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois