Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-06T01:18:56.730Z Has data issue: false hasContentIssue false
  • English
  • Français

Transitive Vector Spaces of Bounded Operators

Published online by Cambridge University Press:  20 November 2018

Sandy Grabiner
Sandy Grabiner*
Affiliation:
Department of Mathematics, Pomona College, Claremont, California, 91711
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.

The linear subspace S of B(X, Y), the space of bounded operators from the Banach space X to the Banach space Y, is said to be transitive if Sx is dense in Y for all x ≠ 0. We give a number of conditions, involving operators intertwined by S, which imply that S is not transitive, and conditions which, when X = Y, imply that the commutant of S is also not transitive.

Keywords

47A1547D15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 381 - 384
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Caradus, S. R., Pfaffenberger, W. E. and Yood, B., Calkin Algebras and Algebras of Operators on Banach Spaces, Dekker, New York, 1974.Google Scholar
2. Fong, C. K., Nordgren, E. A., Radjabalipour, M., Radjavi, H. and Rosenthal, P., Extensions of Lomonosov’s invariant subspace theorem, Acta Sci. Math. (Szeged), 41 (1979), 55–62.Google Scholar
3. Grabiner, S., Operator ranges and invariant subspaces, Indiana U. Math. J., 28 (1979), 845–857.Google Scholar
4. Grabiner, S., Compact endomorphisms and closed ideals in Banach algebras, preprint.Google Scholar
5. Lomonosov, V., Invariant subspaces for operators which commute with a completely continuous operator, Functional Anal. Appl. 7 (1973), 213–214.Google Scholar
6. Nordgren, E., Radjabalipour, M., Radjavi, H. and Rosenthal, P., Algebras intertwining compact operators, Acta Sci. Math. (Szeged), 39 (1977), 115–119.Google Scholar
7. Pearcy, C. and Shields, A. L., A survey of the Lomonosov technique in the theory of invariant subspaces, in Pearcy, C, ed., Topics in Operator Theory, Amer. Math. Soc, Providence, R.I., 1974.Google Scholar