k-TH ROOTS OF p-HYPONORMAL OPERATORS DUGGAL BHAGWATI P.; JEON IN Ho; KO AND EUNGIL;
Abstract
In this paper we prove that if T is a k-th root of a phyponormal operator when T is compact or T is normal for some integer n > k, then T is (generalized) scalar, and that if T is a k-th root of a semi-hyponormal operator and have the property (T) is contained in an angle < 2/k with vertex in the origin, then T is subscalar.
Keywords
k-th roots of p-hyponormal operator;subscalar operator;
Language
English
Cited by
References
1.
A. Aluthge, On p-hyponormal operators for 0 < p < 1, Integral Equations Operator Theory 13 (1990), 307-315
2.
C. Apostol, Spectral decomposition and functional calculus, Rev. Roumaine Math. Pures Appl. 13 (1968), 1481-1528
3.
B. P. Duggal, Quasi-similar p-hyponormal operators, Integral Equations Operator Theory 26 (1996), 338-345
4.
J. Eschmeier, Invariant subspaces for subscalar operators, Arch. Math. 52 (1989), 562-570
5.
M. Fujii, C. Himeji, and A. Matsumoto, Theorems of Ando and Saito for p-hyponormal operators, Math. Japonica 39 (1994), 595-598
6.
T. Furuta, Invitation to linear operators, Taylor & Francis, London and New York, 2001
7.
F. Gilfeather, Operator valued roots of abelian analytic functions, Pacific J. Math. 55 (1974), 127-148
8.
M. Kim and E. Ko, Square roots of hyponormal operators, Glasg. Math. J. 41 (1999), 463-470
9.
E. Ko, On p-hyponormal operators, Proc. Amer. Math. Soc. 128 (2000), 775- 780
10.
K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, London Math. Soc. Monogr. (N.S.) 2000
11.
M. Putinar, Hyponormal operators are subscalar, J. Operator Theory 12 (1984), 385-395
12.
D. Xia, Spectral Theory of Hyponormal Operators, Birkhauser Verlag, Boston, 1983