Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T07:33:47.563Z Has data issue: false hasContentIssue false
  • English
  • Français

Simultaneous Triangularization of Algebras of Polynomially Compact Operators

Published online by Cambridge University Press:  20 November 2018

M. Radjabalipour
M. Radjabalipour*
Affiliation:
Department of Mathematics, University of Kerman, Kerman, Iran
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.

If A is a norm closed algebra of compact operators on a Hilbert space and if its Jacobson radical J(A) consists of all quasinilpotent operators in A then A/ J(A) is commutative. The result is not valid for a general algebra of polynomially compact operators.

Keywords

47B0547D25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 2 , 01 June 1991 , pp. 260 - 264
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Grabiner, S., The nilpotency of Banach algebras, Proc. Amer. Math. Soc. 21 (1969), 510.Google Scholar
2. Hadwin, D., Radjavi's trace condition for triangularizability, J. Algebra 109 (1987), 184–192.Google Scholar
3. Hadwin, D., Nordgren, E., M. Radjabalipour, Radjavi, H., and Rosenthal, P., On simultaneous triangularization of collection of operators, to appear.Google Scholar
4. Lomonosov, V. I., Invariant subspaces for operators commuting with compact operators, Functional Anal. Appl. 7 (1973), 213–214.Google Scholar
5. Laurie, C., Nordgren, E., H. Radjavi, and Rosenthal, P., On triangularization of algebras of operators, J. Reine Angew. Math. 327 (1981), 143–155.Google Scholar
6. Murphy, G., Triangularizable algebras of compact operators, Proc. Amer. Math. Soc. 84 (1982), 143–155.Google Scholar
7. Radjavi, H. and Rosenthal, P., Invariant Subspaces, Springer-Verlag, New York, Heidelberg, Berlin, 1973.Google Scholar
8. Ringrose, J. R., Super-diagonal forms for compact linear operators, Proc. London Math. Soc. (3) 12 ( 1962), 367–384.Google Scholar
9. Ringrose, J. R., “Compact Non-self-adjoint Operators,” Van Nostrand, New York, 1971.Google Scholar