Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$k$-hyponormality of powers of weighted shifts via Schur products


Authors: Raúl Curto and Sang Soo Park
Journal: Proc. Amer. Math. Soc. 131 (2003), 2761-2769
MSC (1991): Primary 47B37, 47B20; Secondary 47-04, 47A13
Published electronically: November 13, 2002
MathSciNet review: 1974333
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize $k$-hyponormality and quadratic hyponormality of powers of weighted shifts using Schur product techniques.


References [Enhancements On Off] (What's this?)

  • [Ath] A. Athavale, On joint hyponormality of operators, Proc. Amer. Math. Soc 103(1988), 417-423. MR 89f:47033
  • [BEJ] J. Bae, G. Exner and I.B. Jung, Criteria for positively quadratically hyponormal weighted shifts, Proc. Amer. Math. Soc., to appear.
  • [Bra] J. Bram, Subnormal operators, Duke Math. J. 22(1955), 75-94. MR 16:835a
  • [Con] J.B. Conway, Subnormal Operators, Research Notes in Mathematics, vol. 51, Pitman Publ. Co., London, 1981. MR 83i:47030
  • [Cu1] R. Curto, Quadratically hyponormal weighted shifts, Integral Equations Operator Theory 13(1990), 49-66. MR 90k:47061
  • [Cu2] R. Curto, Joint hyponormality: A bridge between hyponormality and subnormality, Proc. Symposia Pure Math. 51(1990), 69-91. MR 91k:47049
  • [CF1] R. Curto and L. Fialkow, Recursiveness, positivity, and truncated moment problems, Houston J. Math. 17(1991), 603-635. MR 93a:47016
  • [CF2] R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equations Operator Theory 17(1993), 202-246. MR 94h:47050
  • [CF3] R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, II, Integral Equations Operator Theory 18(1994), 369-426. MR 94m:47044
  • [CJ] R. Curto and I.B. Jung, Quadratically hyponormal weighted shifts with two equal weights, Integral Equations Operator Theory 37(2000), 208-231. MR 2001h:47046
  • [CJL] R. Curto, I.B. Jung and W.Y. Lee, Extension and extremality of recursively generated weighted shifts, Proc. Amer. Math. Soc. 130(2002), 565-576. MR 2002i:47041
  • [CP1] R. Curto and M. Putinar, Existence of non-subnormal polynomially hyponormal operators, Bull. Amer. Math. Soc. 25(1991), 373-378. MR 93e:47028
  • [CP2] R. Curto and M. Putinar, Nearly subnormal operators and moment problems, J. Functional Analysis 115(1993), 480-497. MR 95d:47024
  • [CMX] R. Curto, P.S. Muhly and J. Xia, Hyponormal pairs of commuting operators, Operator Theory: Adv. Appl. 35(1988), 1-22. MR 90m:47037
  • [JL] I.B. Jung and C. Li, A formula for $k$-hyponormality of backstep extensions of subnormal weighted shifts, Proc. Amer. Math. Soc. 129(2001), 2343-2351. MR 2002b:47061
  • [JP1] I.B. Jung and S. Park, Quadratically hyponormal weighted shifts and their examples, Integral Equations and Operator Theory 36(2000), 480-498. MR 2001i:47051
  • [JP2] I.B. Jung and S. Park, Cubically hyponormal weighted shifts and their examples, J. Math. Anal. Appl. 247(2000), 557-569. MR 2001h:47047
  • [McCP] S. McCullough and V. Paulsen, A note on joint hyponormality, Proc. Amer. Math. Soc. 107(1989), 187-195. MR 90a:47062
  • [Pau] V. Paulsen, Completely bounded maps and dilations, Pitman Research Notes in Mathematics Series, vol. 146, Longman Sci. Tech., New York, 1986. MR 88h:46111
  • [Sta] J. Stampfli, Which weighted shifts are subnormal, Pacific J. Math. 17(1996), 367-379. MR 33:1740
  • [Shi] A. Shields, Weighed shift operators and analytic function theory, Math. Surveys, No. 13, Amer. Math. Soc., 1974. MR 50:14341
  • [Wol] S. Wolfram, The Mathematica book, Version 3.0, Wolfram Media Inc., Champaign, IL, 1996. MR 97d:35003

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47B37, 47B20, 47-04, 47A13

Retrieve articles in all journals with MSC (1991): 47B37, 47B20, 47-04, 47A13


Additional Information

Raúl Curto
Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
Email: curto@math.uiowa.edu

Sang Soo Park
Affiliation: Department of Mathematics, Kyungpook National University, Deagu, Korea
Email: pss4855@hanmail.net

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06805-3
PII: S 0002-9939(02)06805-3
Keywords: $k$-hyponormality, powers of weighted shifts, Schur products
Received by editor(s): October 5, 2001
Received by editor(s) in revised form: March 27, 2002
Published electronically: November 13, 2002
Additional Notes: The research of the first author was partially supported by NSF grant DMS-9800931
The research of the second author was partially supported by KOSEF research project no. R01-2000-00003
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society