Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T19:37:14.107Z Has data issue: false hasContentIssue false
  • English
  • Français

Dividing in the algebra of compact operators

Published online by Cambridge University Press:  12 March 2014

Alexander Berenstein
Alexander Berenstein*
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801-2975., USA, E-mail: aberenst@math.uiuc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract.

We interpret the algebra of finite rank operators as imaginaries inside a Hilbert space. We prove that the Hilbert space enlarged with these imaginaries has built-in canonical bases.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 3 , September 2004 , pp. 817 - 829
Copyright
Copyright © Association for Symbolic Logic 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Akhiezer, N. I. and Glazman, I. M., Theory of Linear Operators in Hilbert Space, Vol I and Vol II, Monographs and Studies in Mathematics, vol. 10, Pitman (Advanced Publishing Program), Boston, Massachusetts, London, 1981.Google Scholar
[2]Ben-Yaacov, Itay, Positive model theory and compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), no. 1, pp. 85–118.CrossRefGoogle Scholar
[3]Ben-Yaacov, Itay, Simplicity in compact abstract theories, Journal of Mathematical Logic, vol. 3 (2003), no. 2, pp. 163–191.CrossRefGoogle Scholar
[4]Ben-Yaacov, Itay and Berenstein, Alexander, Imaginaries in Hilbert spaces, Archive for Mathematical Logic, to appear.Google Scholar
[5]Berenstein, Alexander and Buechler, Steven, Homogeneous expansions of Hilbert spaces, Annals of Pure and Applied Logic, to appear.Google Scholar
[6]Buechler, Steven and Lessmann, Oliver, Simple Homogeneous models, Journal of the American Mathematical Society, vol. 16 (2003), no. 1, pp. 91–121.CrossRefGoogle Scholar
[7]Henson, Ward and Iovino, Jose, Ultraproducts in analysis, Analysis and Logic, London Mathematical Society Lecture Notes Series, 2002.Google Scholar
[8]Iovino, Jose, Stable Banach spaces and Banach space structures, I. Fundamentals, Models, Algebras, and Proofs (Bogotá, 1995), Lectures Notes in Pure and Applied Mathematics, vol. 203, Dekker, New York, 1999, pp. 77–95.Google Scholar
[9]Murphy, Gerard, C*Algebras and Operator Theory, Academic Press, 1990.Google Scholar