Criteria for positively quadratically hyponormal weighted shifts

Bae, Ju Youn; Jung, Il; Exner, George

doi:10.1090/S0002-9939-02-06493-6

Criteria for positively quadratically hyponormal weighted shifts
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by Ju Youn Bae, Il Bong Jung and George R. Exner PDF

Proc. Amer. Math. Soc. 130 (2002), 3287-3294 Request permission

Abstract:

For bounded linear operators on Hilbert space, positive quadratic hyponormality is a property strictly between subnormality and hyponormality and which is of use in exploring the gap between these more familiar properties. Recently several related positively quadratically hyponormal weighted shifts have been constructed. In this note we establish general criteria for the positive quadratic hyponormality of weighted shifts which easily yield the results for these examples and other such weighted shifts.

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