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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: 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

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