Skip to main content

Generations of von Neumann algebras

Part of the Lecture Notes in Mathematics book series (LNM,volume 247)

Keywords

  • Separable Hilbert Space
  • Single Operator
  • Partial Isometry
  • Strong Operator Topology
  • Maximal Ideal Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Behncke, Generators of W*-algebras, Tôhoku Math. J. 22(1970), 541–546.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. ____, Generators of W*-algebras III, to appear.

    Google Scholar 

  3. C. Davis, Generators of the ring of all bounded operators, Proc. Amer. Math. Soc. 6(1955), 970–972.

    CrossRef  MATH  Google Scholar 

  4. D. Deckard and C. Pearcy, On matrices over the ring of continuous complex valued functions on a Stonian space, Proc. Amer. Math. Soc. 14(1963), 322–328.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien, Gauthier-Villars, Paris (dieuxième édition), 1969.

    MATH  Google Scholar 

  6. R. G. Douglas and C. Pearcy, Von Neumann algebras with a single generator, Michigan Math. J. 16(1969), 21–26.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. ____ and D. M. Topping, Operators whose squares are zero, Rev. Romaine Math. Pures Appl. 12(1967), 647–652.

    MathSciNet  MATH  Google Scholar 

  8. P. A. Fillmore, On products of symmetries, Canadian J. Math. 18(1966), 897–900.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. ____ and D. M. Topping, Operator algebras generated by projections, Duke Math. J. 34(1967), 333–336.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. P. R. Halmos, Normal dilations and extensions of operators, Summa Braisilliensis Math. 2(1950), 125–154.

    MathSciNet  Google Scholar 

  11. ____, Hilbert space problem book, van Nostrand, 1967.

    Google Scholar 

  12. J. von Neumann, Zur Algebra der Funktionaloperationen und Theorie der Normalen Operatoren, Math. Ann. 102(1929), 370–427.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. C. Pearcy, W*-algebras with a single generator, Proc. Amer. Math. Soc. 13(1962), 831–832.

    MathSciNet  MATH  Google Scholar 

  14. _____, On certain von Neumann algebras which are generated by partial isometries, Proc. Amer. Math. Soc. 15(1964), 393–395.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. _____ and D. M. Topping, Sums of small numbers of idempotents, Michigan Math. J. 14(1967), 453–467.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. R. Powers, Representations of uniformly hyperfinite algebras, Ann. of Math. 86(1967), 138–171.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. B. Russo, Unimodular contractions in Hilbert space, Pacific J. Math. 26(1968), 163–169.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. T. Saitô, Generators of certain von Neumann algebras, Tôhoku Math. J. 20(1968), 101–105.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. _____, On generators of von Neumann algebras, Michigan Math. J. 15(1968), 373–376.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. N. Suzuki and T. Saitô, On the operators which generate continuous von Neumann algebras, Tôhoku Math. J. 15(1963), 277–280.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. D. M. Topping, Transcendental quasi-nilpotents in operator algebras, J. Functional Analysis, 2(1968), 342–351.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. _____, Lectures on von Neumann algebras, 1969.

    Google Scholar 

  23. W. Wogen, On generators for von Neumann algebras, Thesis at Indiana University, 1969.

    Google Scholar 

  24. _____, On generators for von Neumann algebras, Bull. Amer. Math. Soc. 75(1969), 95–99.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. T. Yoshino, Subnormal operators with a cyclic vector, Tôhoku Math. J. 21(1969), 47–55.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1972 Springer-Verlag

About this paper

Cite this paper

Saitô, T. (1972). Generations of von Neumann algebras. In: Lectures on Operator Algebras. Lecture Notes in Mathematics, vol 247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058556

Download citation

  • DOI: https://doi.org/10.1007/BFb0058556

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05729-1

  • Online ISBN: 978-3-540-37117-5

  • eBook Packages: Springer Book Archive