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Recursively generated weighted shifts and the subnormal completion problem. II. (English) Zbl 0807.47016
Summary: Recursively generated weighted shifts are employed to exhibit a large collection of quadratically hyponormal shifts which are not subnormal. This result is reached after analyzing 1-step extensions of recursive subnormal completions generated from three-weight data. The techniques make use of the subnormal completion criterion, and allow us to obtain additional criteria to distinguish between the various classes of \(k\)- hyponormal weighted shifts. Applications to bilateral shifts are also included.
[For part I see ibid. 17, No. 2, 202-246 (1993)].

MSC:
47B20 Subnormal operators, hyponormal operators, etc.
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A20 Dilations, extensions, compressions of linear operators
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