The range of operators on von Neumann algebras

Details The range of operators on von Neumann algebras The range of operators on von Neumann algebras

2001-04-11

arxiv.org/abs/math/0104119v1

Mathematics

Operator Algebras

8 pages

Scientific paper

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.

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