Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2010, Article ID 713563, 33 pages
http://dx.doi.org/10.1155/2010/713563
Research Article

Extension of Spectral Scales to Unbounded Operators

Department of Mathematics, Weber State University, Ogden, UT 84404, USA

Received 30 May 2010; Accepted 14 June 2010

Academic Editor: Palle E. Jorgensen

Copyright © 2010 M. D. Wills. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. A. Akemann, J. Anderson, and N. Weaver, “A geometric spectral theory for n-tuples of self-adjoint operators in finite von Neumann algebras,” Journal of Functional Analysis, vol. 165, no. 2, pp. 258–292, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  2. R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras. Vol. I: Elementary Theory, vol. 15 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 1997. View at MathSciNet
  3. D. Petz, “Spectral scale of selfadjoint operators and trace inequalities,” Journal of Mathematical Analysis and Applications, vol. 109, no. 1, pp. 74–82, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras. Vol. II: Advanced Theory, vol. 16 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 1997. View at MathSciNet
  5. M. Takesaki, Theory of Operator Algebras. I, Springer-Verlag, New York, NY, USA, 1979. View at MathSciNet
  6. C. A. Akemann and J. Anderson, “The spectral scale and the k-numerical range,” Glasgow Mathematical Journal, vol. 45, no. 2, pp. 225–238, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. C. A. Akemann and J. Anderson, “The spectral scale and the numerical range,” International Journal of Mathematics, vol. 14, no. 2, pp. 171–189, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. E. Nelson, “Notes on non-commutative integration,” Journal of Functional Analysis, vol. 15, pp. 103–116, 1974. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Reed and B. Simon, Methods of Modern Mathematical Physics. I: Functional Analysis, Academic Press, New York, NY, USA, 2nd edition, 1980. View at MathSciNet
  10. C. A. Akemann and G. K. Pedersen, “Facial structure in operator algebra theory,” Proceedings of the London Mathematical Society, vol. 64, no. 2, pp. 418–448, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. W. Rudin, Real and Complex Analysis, McGraw-Hill Series in Higher Mathematic, McGraw-Hill, New York, NY, USA, 2nd edition, 1974. View at MathSciNet
  12. H. L. Royden, Real Analysis, Macmillan, New York, NY, USA, 3rd edition, 1988. View at MathSciNet
  13. R. G. Bartle, A Modern Theory of Integration, vol. 32 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 2001. View at MathSciNet
  14. E. Kreyszig, Introductory Functional Analysis with Applications, Wiley Classics Library, John Wiley & Sons, New York, NY, USA, 1989. View at MathSciNet
  15. P. Petersen, Riemannian Geometry, vol. 171 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1998. View at MathSciNet