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

Raul Curto·Jasang Yoon
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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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Raul Curto, Jasang Yoon. 2004-05-30. Jointly hyponormal pairs of commuting subnormal operators need not be jointly subnormal. https://arxiv.org/abs/math/0405587

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