Geodesic
A remark concerning Putinar's model of hyponormal weighted shifts
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 1125-1130 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar's construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar's theory does not lead to the extension that would provide a positive answer to the question.
The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar's construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar's theory does not lead to the extension that would provide a positive answer to the question.
DOI : 10.21136/CMJ.2017.0129-17
Classification : 47B20, 47B37
Keywords: weighted shift operator; almost normal operator; hyponormal operator 
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Lauric, Vasile. A remark concerning Putinar's model of hyponormal weighted shifts. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 4, pp. 1125-1130. doi: 10.21136/CMJ.2017.0129-17

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