The range of operators on von Neumann algebras

Authors:
Teresa Bermúdez and N. J. Kalton

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

Published electronically:
October 24, 2001

MathSciNet review:
1879968

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that for every bounded linear operator , where is a non-reflexive quotient of a von Neumann algebra, the point spectrum of is non-empty (i.e., for some the operator fails to have dense range). In particular, and as an application, we obtain that such a space cannot support a topologically transitive operator.

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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

DOI:
https://doi.org/10.1090/S0002-9939-01-06292-X

Keywords:
Grothendieck space,
$L$-embedded space,
von Neumann algebra,
point spectrum,
topologically transitive operator,
hypercyclic operator

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

Article copyright:
© Copyright 2001
American Mathematical Society