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Jointly hyponormal pairs of commuting subnormal operators need not be jointly subnormal. (English) Zbl 1115.47020
The authors 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 conjecture of R. E. Curto, P. S. Muhly and J.–B. Xia [Oper. Theory, Adv. Appl. 35, 1–22 (1988; Zbl 0681.47005)]. They also obtain a sufficient condition under which joint hyponormality does imply joint subnormality.

47B20Subnormal operators, hyponormal operators, etc.
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A13Several-variable spectral theory
28A50Integration and disintegration of measures
44A60Moment problems (integral transforms)
47-04Machine computation, programs (operator theory)
47A20Dilations, extensions and compressions of linear operators