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Multiplication in Riesz Spaces


Rice, Norman Molesworth (1966) Multiplication in Riesz Spaces. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/PZMJ-B369.


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 L1(ф) in L#, and L1(ф) may be regarded as an abstract integral space. A very general form of the Radon-Nikodym theorem can be proved in L1(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 Radon-Nikodym 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):
  • Luxemburg, W. A. J.
Thesis Committee:
  • Unknown, Unknown
Defense Date:10 May 1965
Funding AgencyGrant Number
Woodrow Wilson FoundationUNSPECIFIED
Record Number:CaltechTHESIS:10192015-111930391
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9227
Deposited On:19 Oct 2015 21:32
Last Modified:07 Mar 2024 23:14

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