Skip to main content Accessibility help
×
Home

The Classification of Factors is not Smooth

  • E. J. Woods (a1)

Extract

There is a natural Borel structure on the set F of all factors on a separable Hilbert space [3]. Let denote the algebraic isomorphism classes in F together with the quotient Borel structure. Now that various non-denumerable families of mutually non-isomorphic factors are known to exist [1; 6; 8; 10; 11; 12; 13], the most obvious question to be resolved is whether or not is smooth (i.e. is there a countable family of Borel sets which separate points). We answer this question negatively by an explicit construction.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      The Classification of Factors is not Smooth
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      The Classification of Factors is not Smooth
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      The Classification of Factors is not Smooth
      Available formats
      ×

Copyright

References

Hide All
1. Araki, H. and Woods, E. J., A classification of factors, Publ. Res. Inst. Math. Sci. Ser. A 4 (1968), 51130.
2. Effros, E., Transformation groups and C*-algebras, Ann. of Math. 81 (1965), 3855.
3. Effros, E., The Borel space of von Neumann algebras on a separable Hilbert space, Pacific J. Math. 15 (1965), 1153-1164. 4^ Global structure in von Neumann algebras, Trans. Amer. Math. Soc. 121 (1966), 434454.
5. Glimm, J., Type I C*-algebras, Ann. of Math. 73 (1961), 572612.
6. Krieger, W., On a class of hyperfinite factors that arise from null-recurrent Markov chains, J. Functional Analysis 7 (1971), 2742.
7. Mackey, G. W., Borel structure in groups and their duals, Trans. Amer. Math. Soc. 85 (1957), 134165.
8. McDuff, D., Uncountably many Ui-factors, Ann. of Math. 90 (1969), 372377.
9. Nielsen, O. A., An example of a von Neumann algebra of global type II (to appear).
10. Powers, R. T., Representations of uniformly hyperfinite algebras and their associated von Neumann rings, Ann. of Math. 86 (1967), 138171.
11. Sakai, S., An uncountable number of II1 and II∞-factors, J. Functional Analysis 5 (1970), 236246.
12. Sakai, S., An uncountable family of non-hyperfinite type Ill-factors, Functional analysis (edited by Wilde, C. O., Academic Press, New York, 1970).
13. Williams, J., Non-isomorphic tensor products of von Neumann algebras (to appear).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

The Classification of Factors is not Smooth

  • E. J. Woods (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed