Citation
Rice, Norman Molesworth (1966) Multiplication in Riesz Spaces. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/PZMJB369. https://resolver.caltech.edu/CaltechTHESIS:10192015111930391
Abstract
A.G. Vulih has shown how an essentially unique intrinsic multiplication can be defined in certain types of Riesz spaces (vector lattices) L. In general, the multiplication is not universally defined in L, but L can always be imbedded in a large space L^{#} in which multiplication is universally defined.
If ф is a normal integral in L, then ф can be extended to a normal integral on a large space L_{1}(ф) in L^{#}, and L_{1}(ф) may be regarded as an abstract integral space. A very general form of the RadonNikodym theorem can be proved in L_{1}(ф), and this can be used to give a relatively simple proof of a theorem of Segal giving a necessary and sufficient condition that the RadonNikodym theorem hold in a measure space.
In another application, the multiplication is used to give a representation of certain Riesz spaces as rings of operators on a Hilbert space.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  (Mathematics)  
Degree Grantor:  California Institute of Technology  
Division:  Physics, Mathematics and Astronomy  
Major Option:  Mathematics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  10 May 1965  
Funders: 
 
Record Number:  CaltechTHESIS:10192015111930391  
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:10192015111930391  
DOI:  10.7907/PZMJB369  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  9227  
Collection:  CaltechTHESIS  
Deposited By:  INVALID USER  
Deposited On:  19 Oct 2015 21:32  
Last Modified:  07 Mar 2024 23:14 
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