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$p$-hyponormality is not translation-invariant

Authors: Muneo Cho and Jun Ik Lee
Journal: Proc. Amer. Math. Soc. 131 (2003), 3109-3111
MSC (2000): Primary 47B20, 47B35
Published electronically: December 30, 2002
MathSciNet review: 1993220
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Abstract: In this note we provide an example of a semi-hyponormal Hilbert space operator $T$ for which $T-\lambda $ is not $p$-hyponormal for some $\lambda \in \mathbb{C}$ and all $0 < p \leq \frac{1}{2}$.

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  • [Al] A. Aluthge, On $p$-hyponormal operators for $0<p<1$, Int. Eq. Op. Th. 13 (1990), 307-315. MR 91a:47025
  • [AlW] A. Aluthge and D. Wang, Powers of $p$-hyponormal operators, J. Inequal. Appl. 3 (1999), 279-284. MR 2000m:47028
  • [An] T. Ando, Operators with a norm condition, Acta Sci. Math. (Szeged) 33 (1972), 169-178. MR 47:9334
  • [Ch] M. Cho, Spectral properties of $p$-hyponormal operators, Glasgow Math. J. 36 (1994), 117-122. MR 94m:47043
  • [ChH] M. Cho and T. Huruya, $p$-hyponormal operators $(0<p<\frac{1}{2})$, Commentationes Math. 33 (1993), 23-29. MR 95b:47021
  • [ChI] M. Cho and M. Itoh, Putnam's inequality for $p$-hyponormal operators, Proc. Amer. Math. Soc. 123 (1995), 2435-2440. MR 95j:47027
  • [ChJ] M. Cho and H. Jin, On $p$-hyponormal operators, Nihonkai Math. J. 6 (1995), 201-206. MR 96j:47019
  • [CuL] R.E. Curto and W.Y. Lee, Joint hyponormality of Toeplitz pairs, Memoirs Amer. Math. Soc. 150 (2001). MR 2002c:47042
  • [FaL] D.R. Farenick and W.Y. Lee, Hyponormality and spectra of Toeplitz operators, Trans. Amer. Math. Soc. 348 (1996), 4153-4174. MR 97k:47027
  • [FHM] M. Fujii, R. Nakamoto and H. Watanabe, The Heinz-Kato-Furuta inequality and hyponormal operators, Math. Japonica 39 (1994), 469-472. MR 95k:47033
  • [Xi] D. Xia, Spectral Theory of Hyponormal Operators, Birkhäuser Verlag, Boston, 1983. MR 87j:47036

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Additional Information

Muneo Cho
Affiliation: Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan

Jun Ik Lee
Affiliation: Department of Mathematics, SungKyunKwan University, Suwon 440-746, Korea

Keywords: Semi-hyponormal, $p$-hyponormal, paranormal, translation--invariant
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
Article copyright: © Copyright 2002 American Mathematical Society

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