A condition under which $B=A=U^*BU$ follows from $B\le A\le U^*BU$
HTML articles powered by AMS MathViewer
- by Takateru Okayasu and Yasunori Ueta PDF
- Proc. Amer. Math. Soc. 135 (2007), 1399-1403 Request permission
Abstract:
We will give some sufficient conditions for a $p$-hyponormal operator, $p>0$, to be normal, and a sufficient condition for a triplet of operators $A$, $B$, $U$ with $A$, $B$ self-adjoint and $U$ unitary such that $B\le A\le U^*BU$ necessarily satisfies $B=A=U^*BU$.References
- Tsuyoshi Andô, On hyponormal operators, Proc. Amer. Math. Soc. 14 (1963), 290–291. MR 145353, DOI 10.1090/S0002-9939-1963-0145353-4
- 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
- Muneo Ch\B{o} and Masuo Itoh, Putnam’s inequality for $p$-hyponormal operators, Proc. Amer. Math. Soc. 123 (1995), no. 8, 2435–2440. MR 1246519, DOI 10.1090/S0002-9939-1995-1246519-3
- Hideki Kosaki, On some trace inequalities, Miniconference on probability and analysis (Sydney, 1991) Proc. Centre Math. Appl. Austral. Nat. Univ., vol. 29, Austral. Nat. Univ., Canberra, 1992, pp. 129–134. MR 1188890
- T. Okayasu and Y. Ueta, Some order-like relations concerned with unitary equivalence, to appear.
- C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Z. 116 (1970), 323–330. MR 270193, DOI 10.1007/BF01111839
- 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
Additional Information
- Takateru Okayasu
- Affiliation: Faculty of Science, Yamagata University, Yamagata 990-8560, Japan
- Yasunori Ueta
- Affiliation: Graduate School of Science and Engineering, Yamagata University, Yamagata 990-8560, Japan
- Received by editor(s): August 17, 2005
- Received by editor(s) in revised form: December 1, 2005
- Published electronically: October 27, 2006
- Communicated by: Joseph A. Ball
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1399-1403
- MSC (2000): Primary 47A63; Secondary 47A10, 47A30
- DOI: https://doi.org/10.1090/S0002-9939-06-08595-9
- MathSciNet review: 2276648