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Science in China Series A: Mathematics

, Volume 41, Issue 6, pp 574–581 | Cite as

Real reduction theory

  • Bingren Li
Article
  • 24 Downloads

Abstract

On a Borel bar space (E,B,-), the following concepts are introduced in a suitable way: measurable fields of real Hilbert spaces, real measurable fields of vectors, operators and Von Neumann (VN) algebras: ξ (⋅),a (⋅),M (⋅). Then a satisfactory real reduction theory is obtained: a real VN algebraM can be represented as a direct integral\(M = \int_{\left( {E, - } \right)}^ \oplus {M(t)dv(t)} \) where each VN algebraM(t) in this field will be simpler.

Keywords

real VN algebra real diagonal operator algebra real measurable field of VN algebras real reduction theory 

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References

  1. 1.
    Li, B. R.,Introduction to Operator Algehrus, Singapore: World Sci., 1992Google Scholar
  2. 2.
    Li, M. L., Li, B. R., Abelian real W*-algebras,Acta Math. Sinica, accepted.Google Scholar
  3. 3.
    Li, B. R., Classification of real Von Neurnann algebras (I),Functional Analysis in China, Kluwer, 1996, 322–332Google Scholar
  4. 4.
    Li, B. R., Classification of real Von Neumann algebras (II),Southeast Asian Bull. of Math., accepted.Google Scholar

Copyright information

© Science in China Press 1998

Authors and Affiliations

  • Bingren Li
    • 1
  1. 1.Institute of MathematicsChinese Academy of SciencesBeijingChina

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