Completely Non-Normal Toeplitz Operators

Completely Non-Normal Toeplitz Operators

下载PDF

导出

摘要 In this paper, we show that the hyponormal Toeplitz operator Tφ with trigonometric polynomial symbol φ is either normal or completely non-normal. Moreover, if Tφ is non-normal, then Tφ has a dense set of cyclic vectors. Some general conditions are also considered. In this paper, we show that the hyponormal Toeplitz operator Tφ with trigonometric polynomial symbol φ is either normal or completely non-normal. Moreover, if Tφ is non-normal, then Tφ has a dense set of cyclic vectors. Some general conditions are also considered.

作者 Yah Yue SHI Yu Feng LU

机构地区 School of Mathematical Sciences

出处《Journal of Mathematical Research and Exposition》 CSCD 2011年第4期727-734,共8页 数学研究与评论（英文版）

基金 Supported by the National Natural Science Foundation of China (Grant Nos.10971020 10671028)

关键词 Toeplitz operator completely nononormal hyponormal cyclic. Toeplitz operator completely nononormal hyponormal cyclic.

分类号 O177.1 [理学—基础数学]

引文网络
相关文献

参考文献15

1BEURLING A. On two problems concerning linear transformations in Hilbert space [J]. Acta Math., 1948, 81(1): 239-255.
2BROWN A, HALMOS P R. Algebraic properties of Toeplitz operators [J]. J. Reine Angew. Math., 1963/1964, 213: 89-102.
3CHAN K C, SEUBERT S M. Reducing subspaces of compressed analytic Toeplitz operators on the Hardy space [J]. Integral Equations Operator Theory, 1997, 28(2): 147-157.
4CLANCEY K F, ROGERS D D. Cyclic vectors and seminormaJ operators [J]. Indiana Univ. Math. J., 1978, 27(4): 689-696.
5COBURN L A. Weyl's theorem for nonnormaJ operators [J]. Michigan Math. J., 1966, 13(3): 285-288.
6COWEN C C. Hyponormality of Toeplitz operators [J]. Proc. Amer. Math. Soc., 1988, 103(3): 809-812.
7DOUGLAS R G. Banach Algebra Techniques in Operator Theory (2nd) [M]. Springer-Verlag, New York, 1998.
8FARENICK D R, LEE W Y. Hyponormality and spectra of Toeplitz operators [J]. Trans. Amer. Math. Soc., 1996, 348(10): 4153-4174.
9FARENICK D R, MCEACHIN R. Toepltiz operators hyponormal with the unilateral shift [J]. Integral Equations Operator Theory, 1995, 22(3): 273-280.
10FELDMAN N S. Pure subnormal operators have cyclic adjoints [J]. J. Funet. Anal., 1999, 162(2): 379-399.

1GUO Xun Xiang.Algebraic Properties of Toeplitz Operators on Discrete Commutative Groups[J].Journal of Mathematical Research and Exposition,2008,28(2):396-402.
2Xinmin Lu.Some Properties of Completely Arithmetical Rings[J].Algebra Colloquium,2016,23(1):83-88.
3Yuan Jinyong Department of Mathematics University of Science and Technology of China Hefei, 230027 China.Spectra of Composition Operators on Lummer-Hardy Spaces[J].Acta Mathematica Sinica,English Series,1994,10(2):209-214.
4Hu Jun,He Jianjun,Xu Shiwei,H. Yamaguchi,Ma Peng,D. Kahl,Su Jun,Wang Hongwei,T. Nakao,Y. Wakabayashi,J. Y. Moon,T. Teranishi,H. S. Jung,T. Hashimoto,A. Chen,D. Irvine,S. Kubono.2-13 Stellar Reaction Rate of the 14O(α, p)17F[J].IMP & HIRFL Annual Report,2014(1):45-46.

Journal of Mathematical Research and Exposition

2011年第4期

浏览历史

内容加载中请稍等...

Completely Non-Normal Toeplitz Operators

参考文献15

相关作者

相关机构

相关主题

浏览历史