The range of operators on von Neumann algebras
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- by Teresa Bermúdez and N. J. Kalton PDF
- Proc. Amer. Math. Soc. 130 (2002), 1447-1455 Request permission
Abstract:
We prove that for every bounded linear operator $T:X\to X$, where $X$ is a non-reflexive quotient of a von Neumann algebra, the point spectrum of $T^*$ is non-empty (i.e., for some $\lambda \in \mathbb C$ the operator $\lambda I-T$ fails to have dense range). In particular, and as an application, we obtain that such a space cannot support a topologically transitive operator.References
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Additional Information
- Teresa Bermúdez
- Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Canary Islands, Spain
- Email: tbermude@ull.es
- N. J. Kalton
- Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211-0001
- Email: nigel@math.missouri.edu
- Received by editor(s): November 20, 2000
- Published electronically: October 24, 2001
- Additional Notes: The first author was supported by DGICYT Grant PB 97-1489 (Spain)
The second author was supported by NSF grant DMS-9870027 - Communicated by: Joseph A. Ball
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1447-1455
- MSC (2000): Primary 47A16, 47C15
- DOI: https://doi.org/10.1090/S0002-9939-01-06292-X
- MathSciNet review: 1879968