Jointly hyponormal pairs of commuting subnormal operators need not be jointly subnormal

Authors:
Raúl E. Curto and Jasang Yoon

Journal:
Trans. Amer. Math. Soc. **358** (2006), 5139-5159

MSC (2000):
Primary 47B20, 47B37, 47A13, 28A50; Secondary 44A60, 47-04, 47A20

DOI:
https://doi.org/10.1090/S0002-9947-06-03911-0

Published electronically:
June 15, 2006

MathSciNet review:
2231888

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Abstract | References | Similar Articles | Additional Information

Abstract: We construct three different families of commuting pairs of subnormal operators, jointly hyponormal but not admitting commuting normal extensions. Each such family can be used to answer in the negative a 1988 conjecture of R. Curto, P. Muhly and J. Xia. We also obtain a sufficient condition under which joint hyponormality does imply joint subnormality.

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Additional Information

**Raúl E. Curto**

Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242

Email:
rcurto@math.uiowa.edu

**Jasang Yoon**

Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011

Email:
jyoon@iastate.edu

DOI:
https://doi.org/10.1090/S0002-9947-06-03911-0

Keywords:
Jointly hyponormal pairs,
subnormal pairs,
$2$-variable weighted shifts

Received by editor(s):
January 22, 2004

Received by editor(s) in revised form:
December 5, 2004

Published electronically:
June 15, 2006

Additional Notes:
This research was partially supported by NSF Grant DMS-0099357

Article copyright:
© Copyright 2006
American Mathematical Society