Geodesic
On totally $\ast$-paranormal operators
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 4, pp. 1265-1280
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we study some properties of a totally $\ast $-paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally $\ast $-paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally $\ast $-paranormal operators through the local spectral theory. Finally, we show that every totally $\ast $-paranormal operator satisfies an analogue of the single valued extension property for $W^{2}(D,H)$ and some of totally $\ast $-paranormal operators have scalar extensions.
In this paper we study some properties of a totally $\ast $-paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally $\ast $-paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally $\ast $-paranormal operators through the local spectral theory. Finally, we show that every totally $\ast $-paranormal operator satisfies an analogue of the single valued extension property for $W^{2}(D,H)$ and some of totally $\ast $-paranormal operators have scalar extensions.
Classification : 47A10, 47A11, 47B20, 47B37, 47B38, 47B40
Keywords: hyponormal; totally $\ast $-paranormal; hypercyclic; operators 
@article{CMJ_2006_56_4_a13,
     author = {Ko, Eungil and Nam, Hae-Won and Yang, Youngoh},
     title = {On totally $\ast$-paranormal operators},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1265--1280},
     year = {2006},
     volume = {56},
     number = {4},
     mrnumber = {2280808},
     zbl = {1164.47319},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_4_a13/}
}
TY  - JOUR
AU  - Ko, Eungil
AU  - Nam, Hae-Won
AU  - Yang, Youngoh
TI  - On totally $\ast$-paranormal operators
JO  - Czechoslovak Mathematical Journal
PY  - 2006
SP  - 1265
EP  - 1280
VL  - 56
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2006_56_4_a13/
LA  - en
ID  - CMJ_2006_56_4_a13
ER  - 
%0 Journal Article
%A Ko, Eungil
%A Nam, Hae-Won
%A Yang, Youngoh
%T On totally $\ast$-paranormal operators
%J Czechoslovak Mathematical Journal
%D 2006
%P 1265-1280
%V 56
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2006_56_4_a13/
%G en
%F CMJ_2006_56_4_a13
Ko, Eungil; Nam, Hae-Won; Yang, Youngoh. On totally $\ast$-paranormal operators. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 4, pp. 1265-1280. http://geodesic.mathdoc.fr/item/CMJ_2006_56_4_a13/

[1] C. Apostol, L. A. Fialkow, D. A. Herrero and D. Voiculescu: Approximation of Hilbert space operators, Volume II. Research Notes in Mathematics 102, Pitman, Boston, 1984. | MR

[2] S. C. Arora and J. K. Thukral: On a class of operators. Glasnik Math. 21 (1986), 381–386. | MR

[3] S. K. Berberian: An extension of Weyl’s theorem to a class of not necessarily normal operators. Michigan Math J. 16 (1969), 273–279. | DOI | MR | Zbl

[4] S. K. Berberian: The Weyl’s spectrum of an operator. Indiana Univ. Math. J. 20 (1970), 529–544. | DOI | MR

[5] S. W. Brown: Hyponormal operators with thick spectrum have invariant subspaces. Ann. of Math. 125 (1987), 93–103. | DOI | MR

[6] L. A. Coburn: Weyl’s theorem for non-normal operators. Michigan Math. J. 13 (1966), 285–288. | DOI | MR

[7] I. Colojoara and C. Foias: Theory of generalized spectral operators. Gordon and Breach, New York, 1968. | MR

[8] J. B. Conway: Subnormal operators. Pitman, London, 1981. | MR | Zbl

[9] S. Djordjevic, I. Jeon and E. Ko: Weyl’s theorem through local spectral theory. Glasgow Math. J. 44 (2002), 323–327. | MR

[10] B. P. Duggal: On the spectrum of $p$-hyponormal operators. Acta Sci. Math. (Szeged) 63 (1997), 623–637. | MR | Zbl

[11] J. Eschmeier: Invariant subspaces for subscalar operators. Arch. Math. 52 (1989), 562–570. | DOI | MR | Zbl

[12] P. R. Halmos: A Hilbert space problem book. Springer-Verlag, 1982. | MR | Zbl

[13] R. E. Harte: Invertibility and singularity. Dekker, New York, 1988. | Zbl

[14] C. Kitai: Invariant closed sets for linear operators. Ph.D. Thesis, Univ. of Toronto, 1982.

[15] E. Ko: Algebraic and triangular $n$-hyponormal operators. Proc. Amer. Math. Soc. 123 (1995), 3473–3481. | MR | Zbl

[16] K. B. Laursen: Operators with finite ascent. Pacific J. Math. 152 (1992), 323–336. | DOI | MR | Zbl

[17] K. B. Laursen: Essential spectra through local spectral theory. Proc. Amer. Math. Soc. 125 (1997), 1425–1434. | DOI | MR | Zbl

[18] K. K. Oberai: On the Weyl spectrum. Illinois J. Math. 18 (1974), 208–212. | DOI | MR | Zbl

[19] K. K. Oberai: On the Weyl spectrum (II). Illinois J. Math. 21 (1977), 84–90. | DOI | MR | Zbl

[20] M. Putinar: Hyponormal operators are subscalar. J. Operator Th. 12 (1984), 385–395. | MR | Zbl

[21] R. Lange: Biquasitriangularity and spectral continuity. Glasgow Math. J. 26 (1985), 177–180. | DOI | MR | Zbl

[22] B. L. Wadhwa: Spectral, $M$-hyponormal and decomposable operators. Ph.D. thesis, Indiana Univ., 1971.

[23] D. Xia: Spectral theory of hyponormal operators. Operator Theory 10, Birkhäuser-Verlag, 1983. | MR | Zbl