Criteria for positively quadratically hyponormal weighted shifts

Authors:
Ju Youn Bae, Il Bong Jung and George R. Exner

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3287-3294

MSC (2000):
Primary 47B37, 47B20

Published electronically:
May 29, 2002

MathSciNet review:
1913008

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Ju Youn Bae**

Affiliation:
Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Korea

Email:
baejuyoun@hanmir.com

**Il Bong Jung**

Affiliation:
Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Korea

Email:
ibjung@kyungpook.ac.kr

**George R. Exner**

Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837

Email:
exner@bucknell.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06493-6

Keywords:
Quadratically hyponormal operator,
positively quadratically hyponormal operator,
$k$-hyponormal operator

Received by editor(s):
September 28, 2000

Received by editor(s) in revised form:
June 11, 2001

Published electronically:
May 29, 2002

Additional Notes:
The first and second authors were supported by the Korea Research Foundation Grant (KRF-2000-015-DP0012).

Communicated by:
David R. Larson

Article copyright:
© Copyright 2002
American Mathematical Society