Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T13:40:04.209Z Has data issue: false hasContentIssue false
  • English
  • Français

Positive Powers of Positive Positive Definite Matrices

Published online by Cambridge University Press:  20 November 2018

Lon Rosen
Lon Rosen*
Affiliation:
Mathematics Department University of British Columbia Vancouver, B.C. V6T 1Z2, e-mail: rosen@math.ubc.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let C be an n x n positive definite matrix. If C ≥ 0 in the sense that Cij ≥ 0 and if p > n — 2, then Cp ≥ 0. This implies the following "positive minorant property" for the norms ‖A‖p = [tr(A*A)p/2]1/P. Let 2 < p ≠ 4, 6, … . Then 0 ≤ A ≤ B => ‖A‖p ≥ ‖B‖P if and only if n < p/2 + 1.

Keywords

15A4847A6360J15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 1 , 01 February 1996 , pp. 196 - 209
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Dechamps-Gondim, M., Lust-Piquard, F. and Queffelec, H., On the Minorant Properties in Cp(H), Pac. J. Math. 119(1985), 89–101.Google Scholar
2. Peller, V.V., Dokl. Acad. Nauk. Math. 252(1980), 43–47.Google Scholar
3. Simon, B., Pointwise Domination of Matrices and Comparison of Ip Norms, Pac. J. Math. 97(1981), 471— 475.Google Scholar
4. Weissenhofer, S., University of British Columbia Ph.D. Thesis, 1993.Google Scholar
5. Yosida, K., Functional Analysis. Springer-Verlag, New York, 1968.Google Scholar