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), 51395159
MSC (2000):
Primary 47B20, 47B37, 47A13, 28A50; Secondary 44A60, 4704, 47A20
Published electronically:
June 15, 2006
MathSciNet review:
2231888
Fulltext PDF Free Access
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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:
http://dx.doi.org/10.1090/S0002994706039110
PII:
S 00029947(06)039110
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 DMS0099357
Article copyright:
© Copyright 2006
American Mathematical Society
