hyponormality of powers of weighted shifts via Schur products
Authors:
Raúl Curto and Sang Soo Park
Journal:
Proc. Amer. Math. Soc. 131 (2003), 27612769
MSC (1991):
Primary 47B37, 47B20; Secondary 4704, 47A13
Published electronically:
November 13, 2002
MathSciNet review:
1974333
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: We characterize hyponormality and quadratic hyponormality of powers of weighted shifts using Schur product techniques.
 [Ath]
A. Athavale, On joint hyponormality of operators, Proc. Amer. Math. Soc 103(1988), 417423. 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), 7594. 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), 4966. MR 90k:47061
 [Cu2]
R. Curto, Joint hyponormality: A bridge between hyponormality and subnormality, Proc. Symposia Pure Math. 51(1990), 6991. MR 91k:47049
 [CF1]
R. Curto and L. Fialkow, Recursiveness, positivity, and truncated moment problems, Houston J. Math. 17(1991), 603635. MR 93a:47016
 [CF2]
R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equations Operator Theory 17(1993), 202246. 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), 369426. MR 94m:47044
 [CJ]
R. Curto and I.B. Jung, Quadratically hyponormal weighted shifts with two equal weights, Integral Equations Operator Theory 37(2000), 208231. 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), 565576. MR 2002i:47041
 [CP1]
R. Curto and M. Putinar, Existence of nonsubnormal polynomially hyponormal operators, Bull. Amer. Math. Soc. 25(1991), 373378. MR 93e:47028
 [CP2]
R. Curto and M. Putinar, Nearly subnormal operators and moment problems, J. Functional Analysis 115(1993), 480497. MR 95d:47024
 [CMX]
R. Curto, P.S. Muhly and J. Xia, Hyponormal pairs of commuting operators, Operator Theory: Adv. Appl. 35(1988), 122. MR 90m:47037
 [JL]
I.B. Jung and C. Li, A formula for hyponormality of backstep extensions of subnormal weighted shifts, Proc. Amer. Math. Soc. 129(2001), 23432351. MR 2002b:47061
 [JP1]
I.B. Jung and S. Park, Quadratically hyponormal weighted shifts and their examples, Integral Equations and Operator Theory 36(2000), 480498. MR 2001i:47051
 [JP2]
I.B. Jung and S. Park, Cubically hyponormal weighted shifts and their examples, J. Math. Anal. Appl. 247(2000), 557569. MR 2001h:47047
 [McCP]
S. McCullough and V. Paulsen, A note on joint hyponormality, Proc. Amer. Math. Soc. 107(1989), 187195. 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), 367379. 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
 [Ath]
 A. Athavale, On joint hyponormality of operators, Proc. Amer. Math. Soc 103(1988), 417423. 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), 7594. 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), 4966. MR 90k:47061
 [Cu2]
 R. Curto, Joint hyponormality: A bridge between hyponormality and subnormality, Proc. Symposia Pure Math. 51(1990), 6991. MR 91k:47049
 [CF1]
 R. Curto and L. Fialkow, Recursiveness, positivity, and truncated moment problems, Houston J. Math. 17(1991), 603635. MR 93a:47016
 [CF2]
 R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equations Operator Theory 17(1993), 202246. 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), 369426. MR 94m:47044
 [CJ]
 R. Curto and I.B. Jung, Quadratically hyponormal weighted shifts with two equal weights, Integral Equations Operator Theory 37(2000), 208231. 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), 565576. MR 2002i:47041
 [CP1]
 R. Curto and M. Putinar, Existence of nonsubnormal polynomially hyponormal operators, Bull. Amer. Math. Soc. 25(1991), 373378. MR 93e:47028
 [CP2]
 R. Curto and M. Putinar, Nearly subnormal operators and moment problems, J. Functional Analysis 115(1993), 480497. MR 95d:47024
 [CMX]
 R. Curto, P.S. Muhly and J. Xia, Hyponormal pairs of commuting operators, Operator Theory: Adv. Appl. 35(1988), 122. MR 90m:47037
 [JL]
 I.B. Jung and C. Li, A formula for hyponormality of backstep extensions of subnormal weighted shifts, Proc. Amer. Math. Soc. 129(2001), 23432351. MR 2002b:47061
 [JP1]
 I.B. Jung and S. Park, Quadratically hyponormal weighted shifts and their examples, Integral Equations and Operator Theory 36(2000), 480498. MR 2001i:47051
 [JP2]
 I.B. Jung and S. Park, Cubically hyponormal weighted shifts and their examples, J. Math. Anal. Appl. 247(2000), 557569. MR 2001h:47047
 [McCP]
 S. McCullough and V. Paulsen, A note on joint hyponormality, Proc. Amer. Math. Soc. 107(1989), 187195. 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), 367379. 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,
4704,
47A13
Retrieve articles in all journals
with MSC (1991):
47B37,
47B20,
4704,
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/S0002993902068053
PII:
S 00029939(02)068053
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 DMS9800931
The research of the second author was partially supported by KOSEF research project no. R01200000003
Communicated by:
Joseph A. Ball
Article copyright:
© Copyright 2002
American Mathematical Society
