$p$-hyponormal operators are subscalar
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- by Lin Chen, Ruan Yingbin and Yan Zikun PDF
- Proc. Amer. Math. Soc. 131 (2003), 2753-2759 Request permission
Abstract:
We prove that if $R, S\in B(\mathbf {X }),\ R, S$ are injective, then $RS$ is subscalar if and only if $SR$ is subscalar. As corollaries, it is shown that $p$-hyponormal operators $(0<p\le 1)$ and log-hyponormal operators are subscalar; also w-hyponormal operators $T$ with Ker$T\subset$ Ker$T^{*}$ and their generalized Aluthge transformations $T(r, 1-r) \ (0<r<1)$ are subscalar.References
- Jörg Eschmeier and Mihai Putinar, Bishop’s condition $(\beta )$ and rich extensions of linear operators, Indiana Univ. Math. J. 37 (1988), no. 2, 325–348. MR 963505, DOI 10.1512/iumj.1988.37.37016
- Ion Colojoară and Ciprian Foiaş, Theory of generalized spectral operators, Mathematics and its Applications, Vol. 9, Gordon and Breach Science Publishers, New York-London-Paris, 1968. MR 0394282
- Ariyadasa Aluthge, On $p$-hyponormal operators for $0<p<1$, Integral Equations Operator Theory 13 (1990), no. 3, 307–315. MR 1047771, DOI 10.1007/BF01199886
- Daoxing Xia, Spectral theory of hyponormal operators, Operator Theory: Advances and Applications, vol. 10, Birkhäuser Verlag, Basel, 1983. MR 806959, DOI 10.1007/978-3-0348-5435-1
- Kôtarô Tanahashi, On log-hyponormal operators, Integral Equations Operator Theory 34 (1999), no. 3, 364–372. MR 1689394, DOI 10.1007/BF01300584
- Ariyadasa Aluthge and Derming Wang, $w$-hyponormal operators. II, Integral Equations Operator Theory 37 (2000), no. 3, 324–331. MR 1776957, DOI 10.1007/BF01194481
- Mihai Putinar, Hyponormal operators are subscalar, J. Operator Theory 12 (1984), no. 2, 385–395. MR 757441
- Yi Chu, Semihyponormal operators are subscalar, Northeast. Math. J. 4 (1988), no. 2, 145–148. MR 987529
- Lin Chen, Yan Zikun and Ruan Yingbin, Common properties of operators $RS$ and $SR$ and $p$-hyponormal operators, Integr. Equat. Oper. Th. 43 (2002), 313–325.
- Bruce A. Barnes, Common operator properties of the linear operators $RS$ and $SR$, Proc. Amer. Math. Soc. 126 (1998), no. 4, 1055–1061. MR 1443814, DOI 10.1090/S0002-9939-98-04218-X
- Ruan Yingbin and Yan Zikun, Spectral structure and subdecomposability of $p$-hyponormal operators, Proc. Amer. Math. Soc. 128 (2000), no. 7, 2069–2074. MR 1654104, DOI 10.1090/S0002-9939-99-05257-0
- Muneo Ch\B{o} and Tadasi Huruya, $p$-hyponormal operators for $0<p<\frac 12$, Comment. Math. (Prace Mat.) 33 (1993), 23–29. MR 1269396
Additional Information
- Lin Chen
- Affiliation: Department of Mathematics, Fujian Normal University, Fuzhou, 350007, People’s Republic of China
- Ruan Yingbin
- Affiliation: Department of Mathematics, University of Xiamen, Xiamen, 361005, People’s Republic of China
- Email: ruanyingbin@263.net
- Yan Zikun
- Affiliation: Department of Mathematics, Fujian Normal University, Fuzhou, 350007, People’s Republic of China
- Received by editor(s): February 12, 2002
- Published electronically: April 7, 2003
- Additional Notes: This research was supported by the National Natural Science Foundation of China.
- Communicated by: Joseph A. Ball
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2753-2759
- MSC (2000): Primary 47B99, 47A10
- DOI: https://doi.org/10.1090/S0002-9939-03-07011-4
- MathSciNet review: 1974332