Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

A note on $p$-hyponormal operators

Author(s): Tadasi Huruya
Journal: Proc. Amer. Math. Soc. 125 (1997), 3617-3624.
MSC (1991): Primary 47A63, 47B20; Secondary 47A10
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Let $T$ be a $p$-hyponormal operator on a Hilbert space with polar decomposition $T=U|T|$ and let $ \widetilde T=|T|^{t}U|T|^{r-t}$ for $r>0$ and $r \geq t \geq 0.$ We study order and spectral properties of $ \widetilde {T}.$ In particular we refine recent Furuta's result on $p$-hyponormal operators.

References:

1.
A. Aluthge, On $p$-hyponormal operators for 0$<$p$<$1, Integral Equations and Operator Theory 13 (1990), 307-315. MR 91a:47025

2.
J.V. Baxley, Some general conditions implying Weyl's Theorem, Rev. Roum. Math. Pures Appl. 16 (1971), 1163-1166. MR 46:4237

3.
F.F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, Berlin, 1973. MR 54:11013

4.
M. Ch\={o} and T. Huruya, $p$-hyponormal operators for $0<p<1/2$, Comment. Math. 33 (1993), 23-29. MR 95b:47021

5.
M. Ch\={o} and M. Itoh, Putnam's inequality for $p$-hyponormal operators, Proc. Amer. Math. Soc. 123 (1995), 2435-2440. MR 95j:47027

6.
M. Ch\={o}, M. Itoh and S. \={O}shiro, Weyl's theorem holds for $p$-hyponormal operators, Glasgow Math. J. (to appear).

7.
B.P. Duggal, On $p$-hyponormal contractions, Proc. Amer. Math. Soc. 123 (1995), 81-86. MR 95d:47025

8.
T. Furuta, $A\geq B\geq 0$ assures $(B^{r}A^{p}B^{r})^{1/q} \geq B^{(p+2r)/q}$ for $r \geq 0,q \geq 0,q \geq 1$ with $(1+2r)q \geq p+2r$, Proc. Amer. Math. Soc. 101 (1987), 85-88. MR 89b:47028

9.
-, Generalized Aluthge transformation on $p$-hyponormal operators, Proc. Amer. Math. Soc. 124 (1996), 3071-3075. MR 96m:47041

10.
F. Hansen, An operator inequality, Math. Ann. 246 (1980), 325-338. MR 82a:46065

11.
K. Löwner, Über monotone matrixfuncktionen, Math. Z. 38 (1934), 177-216.

12.
S.M. Patel, A note on $p$-hyponormal operators for 0$<$p$<$1, Integral Equations and Operator Theory 21 (1995), 498-503. MR 96c:47033

13.
J.G. Stampfli, Hyponormal operators, Pacific J. Math. 12 (1962), 1453-1458. MR 26:6772

14.
K. Tanahashi, Best possibility of the Furuta inequality, Proc. Amer. Math. Soc. 124 (1996), 141-146. MR 96d:47025

15.
D. Xia, On the non-normal operators-semi-hyponormal operators, Sci. Sinica 23 (1980), 700-713.

16.
-, Spectral Theory of Hyponormal Operators, Birkhäuser Verlag, Basel, 1983. MR 87j:47036

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A63, 47B20, 47A10

Retrieve articles in all Journals with MSC (1991): 47A63, 47B20, 47A10

Additional Information:

Tadasi Huruya
Affiliation: Faculty of Education, Niigata University, Niigata 950-21, Japan
Email: huruya@ed.niigata-u.ac.jp

DOI: 10.1090/S0002-9939-97-04004-5
PII: S 0002-9939(97)04004-5
Keywords: Furuta inequality, hyponormal operator, Weyl spectrum
Received by editor(s): December 28, 1995
Received by editor(s) in revised form: July 12, 1996
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1997, American Mathematical Society

Forward Citation(s):

Information for authors on submitting citations

The following works have cited this article

M. Ch\={o}, M. Itoh and S. \={O}shiro, Weyl's theorem holds for $p$-hyponormal operators, Glasgow Math. J. 39 (1997), 217--220.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google