A hyponormal weighted shift on a directed tree whose square has trivial domain
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- by Zenon Jan Jabłoński, Il Bong Jung and Jan Stochel PDF
- Proc. Amer. Math. Soc. 142 (2014), 3109-3116 Request permission
Abstract:
It is proved that, up to isomorphism, there are only two directed trees that admit a hyponormal weighted shift with nonzero weights whose square has trivial domain. These are precisely those enumerable (i.e., countably infinite) directed trees, one with root, the other without, whose every vertex has an enumerable set of successors. An example of a nonzero hyponormal composition operator in an $L^2$-space whose square has trivial domain is established.References
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Additional Information
- Zenon Jan Jabłoński
- Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6, PL-30348 Kraków, Poland
- Email: Zenon.Jablonski@im.uj.edu.pl
- Il Bong Jung
- Affiliation: Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea
- Email: ibjung@knu.ac.kr
- Jan Stochel
- Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6, PL-30348 Kraków, Poland
- Email: Jan.Stochel@im.uj.edu.pl
- Received by editor(s): May 6, 2011
- Received by editor(s) in revised form: September 18, 2012
- Published electronically: May 21, 2014
- Additional Notes: The research of the first and third authors was supported by the MNiSzW (Ministry of Science and Higher Education) grant No. NN201 546438 (2010-2013)
The second author was supported by the WCU (World Class University) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology (grant No. R32-2009-000-20021-0) - Communicated by: Marius Junge
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 3109-3116
- MSC (2010): Primary 47B37, 47B20; Secondary 47A05
- DOI: https://doi.org/10.1090/S0002-9939-2014-12112-5
- MathSciNet review: 3223367