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

Curto, Raúl; Yoon, Jasang

doi:10.1090/S0002-9947-06-03911-0

Jointly hyponormal pairs of commuting subnormal operators need not be jointly subnormal
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by Raúl E. Curto and Jasang Yoon PDF

Trans. Amer. Math. Soc. 358 (2006), 5139-5159 Request permission

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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