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

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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.
20 pages, 7 figures

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Functional Analysis, Primary 47B20, 47B37, 47A13, 28A50; Secondary 44A60, 47-04, 47A20

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http://salesiana.dossiersoluciones.com/handle/123456789/99270

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0405587
 http://arxiv.org/abs/math/0405587
 Trans. Amer. Math. Soc. 358 (2006), 5139-5159

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arXiv