hyponormality of weighted shifts
Authors:
Scott McCullough and Vern Paulsen
Journal:
Proc. Amer. Math. Soc. 116 (1992), 165169
MSC:
Primary 47B20; Secondary 47B37
MathSciNet review:
1102858
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Abstract: An operator is defined to be hyponormal if the operator matrix is positive, where . In A note on joint hyponormality, Proc. Amer. Math. Soc. 107 (1989), 187195, we proved that hyponormality is equivalent to a Bramtype condition, namely, that the operator matrix is positive. In this note we prove that for weighted shifts, hyponormality is equivalent to an Embrytype condition, namely, that the operator matrix is positive. We give an example to show that this latter condition fails even for a rank one perturbation of a weighted shift. For weighted shifts this Embry condition reduces to the positivity of a sequence of Hankel matrices and we use this reduction to give a new proof of one of the principal results of Curto.
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 S. McCullough and V. I. Paulsen, A note on joint hyponormality, Proc. Amer. Math. Soc. 107 (1989), 187195. MR 972236 (90a:47062)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199211028585
PII:
S 00029939(1992)11028585
Article copyright:
© Copyright 1992 American Mathematical Society
