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Zbl 1115.47020
Curto, Raúl E.; Yoon, Jasang
Jointly hyponormal pairs of commuting subnormal operators need not be jointly subnormal. (English)
[J] Trans. Am. Math. Soc. 358, No. 11, 5139-5159 (2006). ISSN 0002-9947; ISSN 1088-6850/e

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 {\it R.\,E.\thinspace Curto, P.\,S.\thinspace Muhly} and {\it J.--B.\thinspace 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.
[Bahman Yousefi (Shiraz)]

MSC 2000:: *47B20 Subnormal operators, etc.
47B37 Operators on sequence spaces, etc.
47A13 Several-variable spectral theory
28A50 Integration and disintegration of measures
44A60 Moment problems
47-04 Machine computation, programs (operator theory)
47A20 Extensions and related concepts of linear operators

Keywords: jointly hyponormal pairs; subnormal pairs; $2$-variable weighted shifts

Citations: Zbl 0681.47005

Cited in: Zbl 1124.47015 Zbl 1119.47009

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