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

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

Published electronically:
May 29, 2002

MathSciNet review:
1913008

Full-text PDF

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.

**[1]**Y. Choi,*A propagation of quadratically hyponormal weighted shifts*, Bull. Korean Math. Soc.**37**(2000), 347-352. MR**2001h:47045****[2]**Y. Choi, J. Han and W. Lee,*One-step extension of the Bergman shift*, Proc. Amer. Math. Soc.,**128**(2000), 3639-3646. MR**2001b:47037****[3]**Y. Choi and H. Lee,*Two-step extension of the Bergman shift*, Bull. Korean Math. Soc., to appear.**[4]**R. Curto,*Quadratically hyponormal weighted shifts*, Integral Equations Operator Theory**13**(1990), 49-66. MR**90k:47061****[5]**-,*Joint hyponormality: A bridge between hyponormality and subnormality*, Proc. Symposia Pure Math.**51**(1990), Part II, 69-91. MR**91k:47049****[6]**R. Curto and L. Fialkow,*Recursively generated weighted shifts and the subnormal completion problem*, I, Integral Equations Operator Theory**17**(1993), 202-246. MR**94h:47050****[7]**-,*Recursively generated weighted shifts and the subnormal completion problem*, II, Integral Equations Operator Theory**18**(1994), 369-426. MR**94m:47044****[8]**R. Curto and I. Jung,*Quadratically hyponormal weighted shifts with two equal weights*, Integral Equations Operator Theory,**37**(2000), 208-231. MR**2001h:47046****[9]**I. Jung and S. Park,*Quadratically hyponormal weighted shifts and their examples*, Integral Equations Operator Theory,**36**(2000), 480-498. MR**2001i:47051****[10]**W. Lee,*Priviate communication,*1999.**[11]**Wolfram Research, Mathematica, Version 3.0, Wolfram Research Inc., Champaign, IL, 1996.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
47B37,
47B20

Retrieve articles in all journals with MSC (2000): 47B37, 47B20

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