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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new criterion for $k$-hyponormality via weak subnormality


Authors: Raúl E. Curto, Sang Hoon Lee and Woo Young Lee
Journal: Proc. Amer. Math. Soc. 133 (2005), 1805-1816
MSC (2000): Primary 47B20, 47B35, 47A63; Secondary 47B37, 47B38, 47A05, 30D50
Published electronically: December 20, 2004
MathSciNet review: 2120281
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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.


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Additional Information

Raúl E. Curto
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
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
Email: wylee@math.snu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07727-5
PII: S 0002-9939(04)07727-5
Keywords: $k$-hyponormal operators, subnormal operators, Toeplitz operators, unilateral weighted shifts, weak subnormality
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
Article copyright: © Copyright 2004 American Mathematical Society