A new criterion for -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

DOI:
https://doi.org/10.1090/S0002-9939-04-07727-5

Published electronically:
December 20, 2004

MathSciNet review:
2120281

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Abstract | References | Similar Articles | Additional Information

Abstract: In this article we obtain a criterion for -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 -hyponormality and ()-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:
https://doi.org/10.1090/S0002-9939-04-07727-5

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