A new criterion for 𝑘-hyponormality via weak subnormality

Curto, Raúl; Lee, Sang; Lee, Woo

doi:10.1090/S0002-9939-04-07727-5

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ISSN 1088-6826(online) ISSN 0002-9939(print)

A new criterion for -hyponormality via weak subnormality

Authors: Raúl E. Curto, Sang Hoon Lee and Woo Young Lee
Journal: Proc. Amer. Math. Soc. 133 (2005), 1805-1816
MSC (2000): Primary 47B20, 47B35, 47A63; Secondary 47B37, 47B38, 47A05, 30D50
Posted: December 20, 2004
MathSciNet review: 2120281
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Abstract: In this article we obtain a criterion for -hyponormality via weak subnormality. Using this criterion we recapture Spitkovskii's subnormality criterion and give a simple proof of the main result in Gu's preprint (2001), which describes a gap between -hyponormality and ()-hyponormality for Toeplitz operators. In addition, we notice that the minimal normal extension of a subnormal operator is exactly the inductive limit of its minimal partially normal extensions.

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