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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.

MSC:

47B20 Subnormal operators, hyponormal operators, etc.
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A13 Several-variable operator theory (spectral, Fredholm, etc.)
28A50 Integration and disintegration of measures
44A60 Moment problems
47-04 Software, source code, etc. for problems pertaining to operator theory
47A20 Dilations, extensions, compressions of linear operators

Citations:

Zbl 0681.47005

Software:

Mathematica
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Full Text: DOI arXiv

References:

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