$p$ā€“hyponormality is not translationā€“invariant
HTML articles powered by AMS MathViewer
- by Muneo ChŨ and Jun Ik Lee PDF
- Proc. Amer. Math. Soc. 131 (2003), 3109-3111 Request permission
Abstract:
In this note we provide an example of a semi-hyponormal Hilbert space operator $T$ for which $T-\lambda$ is not $p$ā€“hyponormal for some $\lambda \in \mathbb {C}$ and all $0 < p \leq \frac {1}{2}$.References
- Ariyadasa Aluthge, On $p$-hyponormal operators for $0<p<1$, Integral Equations Operator Theory 13 (1990), no.Ā 3, 307ā€“315. MR 1047771, DOI 10.1007/BF01199886
- Ariyadasa Aluthge and Derming Wang, Powers of $p$-hyponormal operators, J. Inequal. Appl. 3 (1999), no.Ā 3, 279ā€“284. MR 1732933, DOI 10.1155/S1025583499000181
- T. Ando, Operators with a norm condition, Acta Sci. Math. (Szeged) 33 (1972), 169ā€“178. MR 320800
- Muneo Ch\B{o}, Spectral properties of $p$-hyponormal operators, Glasgow Math. J. 36 (1994), no.Ā 1, 117ā€“122. MR 1260826, DOI 10.1017/S0017089500030627
- Muneo Ch\B{o} and Tadasi Huruya, $p$-hyponormal operators for $0<p<\frac 12$, Comment. Math. (Prace Mat.) 33 (1993), 23ā€“29. MR 1269396
- Muneo Ch\B{o} and Masuo Itoh, Putnamā€™s inequality for $p$-hyponormal operators, Proc. Amer. Math. Soc. 123 (1995), no.Ā 8, 2435ā€“2440. MR 1246519, DOI 10.1090/S0002-9939-1995-1246519-3
- Muneo Ch\B{o} and Hirohiko Jin, On $p$-hyponormal operators, Nihonkai Math. J. 6 (1995), no.Ā 2, 201ā€“206. MR 1367054
- RaĆŗl E. Curto and Woo Young Lee, Joint hyponormality of Toeplitz pairs, Mem. Amer. Math. Soc. 150 (2001), no.Ā 712, x+65. MR 1810770, DOI 10.1090/memo/0712
- Douglas R. Farenick and Woo Young Lee, Hyponormality and spectra of Toeplitz operators, Trans. Amer. Math. Soc. 348 (1996), no.Ā 10, 4153ā€“4174. MR 1363943, DOI 10.1090/S0002-9947-96-01683-2
- Masatoshi Fujii, Ritsuo Nakamoto, and Hideharu Watanabe, The Heinz-Kato-Furuta inequality and hyponormal operators, Math. Japon. 40 (1994), no.Ā 3, 469ā€“472. MR 1305542
- Daoxing Xia, Spectral theory of hyponormal operators, Operator Theory: Advances and Applications, vol. 10, BirkhƤuser Verlag, Basel, 1983. MR 806959, DOI 10.1007/978-3-0348-5435-1
Additional Information
- Muneo ChŨ
- Affiliation: Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan
- Email: chiyom01@kanagawa-u.ac.jp
- Jun Ik Lee
- Affiliation: Department of Mathematics, SungKyunKwan University, Suwon 440-746, Korea
- Email: jilee@math.skku.ac.kr
- Received by editor(s): February 14, 2000
- Received by editor(s) in revised form: April 26, 2002
- Published electronically: December 30, 2002
- Communicated by: Joseph A. Ball
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3109-3111
- MSC (2000): Primary 47B20, 47B35
- DOI: https://doi.org/10.1090/S0002-9939-02-06865-X
- MathSciNet review: 1993220