Separating classes of composition operators via subnormal condition
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- by Il Bong Jung, Mi Ryeong Lee and Sang Soo Park PDF
- Proc. Amer. Math. Soc. 135 (2007), 3955-3965 Request permission
Abstract:
Several classes have been considered to study the weak subnormalities of Hilbert space operators. One of them is $n$-hypnormality, which comes from the Bram-Halmos criterion for subnormal operators. In this note we consider $E(n)$-hyponormality, which is the parallel version corresponding to the Embry characterization for subnormal operators. We characterize $E(n)$ -hyponormality of composition operators via $k$-th Radon-Nikodym derivatives and present some examples to distinguish the classes.References
- Jim Agler, Hypercontractions and subnormality, J. Operator Theory 13 (1985), no. 2, 203–217. MR 775993
- C. Burnap and I. Jung, Composition operators with weak hyponormality, J. Math. Anal. Appl., to appear.
- Charles Burnap, Il Bong Jung, and Alan Lambert, Separating partial normality classes with composition operators, J. Operator Theory 53 (2005), no. 2, 381–397. MR 2153155
- Raúl E. Curto, Quadratically hyponormal weighted shifts, Integral Equations Operator Theory 13 (1990), no. 1, 49–66. MR 1025673, DOI 10.1007/BF01195292
- Raúl E. Curto, Quadratically hyponormal weighted shifts, Integral Equations Operator Theory 13 (1990), no. 1, 49–66. MR 1025673, DOI 10.1007/BF01195292
- Raúl E. Curto and Lawrence A. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equations Operator Theory 17 (1993), no. 2, 202–246. MR 1233668, DOI 10.1007/BF01200218
- Raúl E. Curto and Lawrence A. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equations Operator Theory 17 (1993), no. 2, 202–246. MR 1233668, DOI 10.1007/BF01200218
- Raúl E. Curto and Lawrence A. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equations Operator Theory 17 (1993), no. 2, 202–246. MR 1233668, DOI 10.1007/BF01200218
- Raúl E. Curto, Sang Hoon Lee, and Jasang Yoon, $k$-hyponormality of multivariable weighted shifts, J. Funct. Anal. 229 (2005), no. 2, 462–480. MR 2183156, DOI 10.1016/j.jfa.2005.03.022
- Raúl E. Curto and Woo Young Lee, Joint hyponormality of Toeplitz pairs, Mem. Amer. Math. Soc. 150 (2001), no. 712, x+65. MR 1810770, DOI 10.1090/memo/0712
- Mary R. Embry, A generalization of the Halmos-Bram criterion for subnormality, Acta Sci. Math. (Szeged) 35 (1973), 61–64. MR 328652
- Mary Embry-Wardrop and Alan Lambert, Subnormality for the adjoint of a composition operator on $L^2$, J. Operator Theory 25 (1991), no. 2, 309–318. MR 1203036
- G. Exner, On $n$-contractive and $n$-hypercontractive operators, Integral Equations Operator Theory, 56 (2006), 451–468.
- G. Exner, I. Jung, and S. Park, On $n$-hypercontractive operators, II, submitted.
- Takayuki Furuta, Invitation to linear operators, Taylor & Francis Group, London, 2001. From matrices to bounded linear operators on a Hilbert space. MR 1978629, DOI 10.1201/b16820
- Masatoshi Ito and Takeaki Yamazaki, Relations between two inequalities $(B^{\frac r2}A^pB^{\frac r2})^{\frac r{p+r}}\geq B^r$ and $A^p\geq (A^{\frac p2}B^rA^{\frac p2})^{\frac p{p+r}}$ and their applications, Integral Equations Operator Theory 44 (2002), no. 4, 442–450. MR 1942034, DOI 10.1007/BF01193670
- Il Bong Jung, Eungil Ko, Chunji Li, and Sang Soo Park, Embry truncated complex moment problem, Linear Algebra Appl. 375 (2003), 95–114. MR 2013458, DOI 10.1016/S0024-3795(03)00617-7
- I. Jung, C. Li and S. Park, Complex moment matrices via Halmos-Bram and Embry conditions, J. Korean Math. Soc., to appear.
- Il Bong Jung and Chunji Li, A formula for $k$-hyponormality of backstep extensions of subnormal weighted shifts, Proc. Amer. Math. Soc. 129 (2001), no. 8, 2343–2351. MR 1823917, DOI 10.1090/S0002-9939-00-05844-5
- Alan Lambert, Hyponormal composition operators, Bull. London Math. Soc. 18 (1986), no. 4, 395–400. MR 838810, DOI 10.1112/blms/18.4.395
- Scott McCullough and Vern Paulsen, A note on joint hyponormality, Proc. Amer. Math. Soc. 107 (1989), no. 1, 187–195. MR 972236, DOI 10.1090/S0002-9939-1989-0972236-8
- Scott McCullough and Vern Paulsen, $k$-hyponormality of weighted shifts, Proc. Amer. Math. Soc. 116 (1992), no. 1, 165–169. MR 1102858, DOI 10.1090/S0002-9939-1992-1102858-5
- M. M. Rao, Conditional measures and applications, Monographs and Textbooks in Pure and Applied Mathematics, vol. 177, Marcel Dekker, Inc., New York, 1993. MR 1234936
- Jung Woi Park and Sang Soo Park, On $k$-hyponormal weighted translation semigroups, Bull. Korean Math. Soc. 39 (2002), no. 4, 527–534. MR 1938992, DOI 10.4134/BKMS.2002.39.4.527
- J. A. Shohat and J. D. Tamarkin, The Problem of Moments, American Mathematical Society Mathematical Surveys, Vol. I, American Mathematical Society, New York, 1943. MR 0008438, DOI 10.1090/surv/001
- R. K. Singh and J. S. Manhas, Composition operators on function spaces, North-Holland Mathematics Studies, vol. 179, North-Holland Publishing Co., Amsterdam, 1993. MR 1246562, DOI 10.1016/S0304-0208(08)71589-5
Additional Information
- Il Bong Jung
- Affiliation: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702-702 Korea
- Email: ibjung@knu.ac.kr
- Mi Ryeong Lee
- Affiliation: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702-702 Korea
- Email: lmr67@yumail.ac.kr
- Sang Soo Park
- Affiliation: Institute of Mathematical Science, Ewha Womans University, Seoul, 120-750, Korea
- Email: pss4855@ewha.ac.kr
- Received by editor(s): June 14, 2006
- Received by editor(s) in revised form: November 7, 2006
- Published electronically: June 19, 2007
- Communicated by: Joseph A. Ball
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 3955-3965
- MSC (2000): Primary 47B20, 47B33; Secondary 47A63
- DOI: https://doi.org/10.1090/S0002-9939-07-09003-X
- MathSciNet review: 2341946