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

Author(s): Raúl E. Curto; Sang Hoon Lee; Woo Young Lee
Journal: Proc. Amer. Math. Soc. 133 (2005), 1805-1816.
MSC (2000): Primary 47B20, 47B35, 47A63; Secondary 47B37, 47B38, 47A05, 30D50
Posted: December 20, 2004
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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: 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
Posted: 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 of article: Copyright 2004, American Mathematical Society

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