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

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

2004-05-30

arxiv.org/abs/math/0405587v1

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

Mathematics

Functional Analysis

20 pages, 7 figures

Scientific paper

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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