On residualities in the set of Markov operators on $\mathcal {C}_1$
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- by Wojciech Bartoszek and Beata Kuna PDF
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Abstract:
We show that the set of those Markov operators on the Schatten class $\mathcal {C}_1$ such that $\lim _{n \to \infty } \| P^n - Q \| = 0$, where $Q$ is one-dimensional projection, is norm open and dense. If we require that the limit projections must be on strictly positive states, then such operators $P$ form a norm dense $G_{\delta }$. Surprisingly, for the strong operator topology operators the situation is quite the opposite.References
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Additional Information
- Wojciech Bartoszek
- Affiliation: Department of Mathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80 952 Gdańsk, Poland
- Beata Kuna
- Affiliation: Department of Mathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80 952 Gdańsk, Poland
- Received by editor(s): May 16, 2003
- Received by editor(s) in revised form: April 7, 2004
- Published electronically: February 15, 2005
- Additional Notes: The authors thank the referee for pointing out a gap in the first version of the proof of Theorem 2.6
- Communicated by: Joseph A. Ball
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 2119-2129
- MSC (2000): Primary 46L55, 47A35; Secondary 37A55, 47B60
- DOI: https://doi.org/10.1090/S0002-9939-05-07776-2
- MathSciNet review: 2137879