A new criterion for $k$-hyponormality via weak subnormality
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- by Raúl E. Curto, Sang Hoon Lee and Woo Young Lee PDF
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Abstract:
In this article we obtain a criterion for $k$-hyponormality via weak subnormality. Using this criterion we recapture Spitkovskii’s subnormality criterion and give a simple proof of the main result in Gu’s preprint (2001), which describes a gap between $k$-hyponormality and ($k+1$)-hyponormality for Toeplitz operators. In addition, we notice that the minimal normal extension of a subnormal operator is exactly the inductive limit of its minimal partially normal extensions.References
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Additional Information
- Raúl E. Curto
- Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
- MR Author ID: 53500
- Email: rcurto@math.uiowa.edu
- Sang Hoon Lee
- Affiliation: Department of Mathematics, Seoul National University, Seoul 151-742, Korea
- Email: shlee@math.skku.ac.kr
- Woo Young Lee
- Affiliation: Department of Mathematics, Seoul National University, Seoul 151-742, Korea
- MR Author ID: 263789
- Email: wylee@math.snu.ac.kr
- Received by editor(s): August 31, 2003
- Received by editor(s) in revised form: February 23, 2004
- Published electronically: December 20, 2004
- Additional Notes: The work of the first-named author was partially supported by NSF research grants DMS-9800931 and DMS-0099357.
The work of the third-named author was partially supported by KOSEF research project No. R01-2000-00003-0 - Communicated by: David R. Larson
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 1805-1816
- MSC (2000): Primary 47B20, 47B35, 47A63; Secondary 47B37, 47B38, 47A05, 30D50
- DOI: https://doi.org/10.1090/S0002-9939-04-07727-5
- MathSciNet review: 2120281