|
On the Helton class of -hyponormal operators
Author(s):
Yoenha
Kim;
Eungil
Ko;
Ji
Eun
Lee
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2113-2120.
MSC (2000):
Primary 47B20;
Secondary 47A10
Posted:
February 28, 2007
MathSciNet review:
2299488
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we show that the Helton class of -hyponormal operators has scalar extensions. As a corollary we get that each operator in the Helton class of  -hyponormal operators has a nontrivial invariant subspace if its spectrum has its interior in the plane.
References:
-
- 1.
- J. Agler, Sub-Jordan operators: Bishop's theorem, spectral inclusion, and spectral sets, J. Operator Theory 7(1982), 373-395. MR 0658619 (83j:47009)
- 2.
- A. Aluthge, On -hyponormal operators for
 , Int. Eq. Op. Th. 13(1990), 307-315. MR 1047771 (91a:47025) - 3.
- J.A. Ball and J.W. Helton, Nonnormal dilations, disconjugacy and constrained spectral factorization, Int. Eq. Op. Th. 3(1980), 216-309. MR 0577164 (83a:47007)
- 4.
- E. Bishop, A duality theorem for an arbitrary operator, Pacific J. Math. 9(1959), 379-397. MR 0117562 (22:8339)
- 5.
- I. Colojoara and C. Foias, Theory of generalized spectral operators, Gordon and Breach, New York, 1968. MR 0394282 (52:15085)
- 6.
- J.B. Conway, Subnormal operators, Pitman Adv. Pub. Program, 1981. MR 0634507 (83i:47030)
- 7.
- J. Eschmeier, Invariant subspaces for subscalar operators, Arch. Math. 52(1989), 562-570. MR 1007631 (90h:47016)
- 8.
- J.W. Helton, Operators with a representation as multiplication by
 on a Sobolev space, Colloquia Math. Soc. Janos Bolyai 5, Hilbert Space Operators, Tihany, Hungary (1970), 279-287. MR 0367687 (51:3929) - 9.
- J.W. Helton, Infinite dimensional Jordan operators and Sturm-Liouville conjugate point theory, Trans. Amer. Math. Soc. 170(1972), 305-331. MR 0308829 (46:7943)
- 10.
- E. Ko, On
 -hyponormal operators, Proc. Amer. Math. Soc. 128(2000), 775-780. MR 1707152 (2000e:47040) - 11.
- E. Ko, w-Hyponormal operators have scalar extensions, Int. Eq. Op. Th. 53(2005), 363-372. MR 2186096 (2006g:47033)
- 12.
- R. Lange and S. Wang, New approaches in spectral decomposition, Contemporary Math. 128, Amer. Math. Soc., 1992. MR 1162741 (93i:47039)
- 13.
- K. Löwner, Über monotone matrix funktionen, Math. Z. 38(1934), 177-216.
- 14.
- M. Putinar, Hyponormal operators are subscalar, J. Operator Theory 12(1984), 385-395. MR 0757441 (85h:47027)
- 15.
- D. Xia, Spectral theory of hyponormal operators, Op. Th.: Adv. Appl. 10, Birkhäuser Verlag, Basel, 1983. MR 0806959 (87j:47036)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
47B20,
47A10
Retrieve articles in all Journals with
MSC (2000):
47B20,
47A10
Additional Information:
Yoenha
Kim
Affiliation:
Department of Mathematics, Ewha Women's University, Seoul 120-750, Korea
Email:
yoenha@ewhain.net
Eungil
Ko
Affiliation:
Department of Mathematics, Ewha Women's University, Seoul 120-750, Korea
Email:
eiko@ewha.ac.kr
Ji
Eun
Lee
Affiliation:
Department of Mathematics, Ewha Women's University, Seoul 120-750, Korea
Email:
jieun7@ewhain.net
DOI:
10.1090/S0002-9939-07-08708-4
PII:
S 0002-9939(07)08708-4
Received by editor(s):
December 14, 2004
Received by editor(s) in revised form:
March 13, 2006
Posted:
February 28, 2007
Additional Notes:
This work was supported by a grant (R14-2003-006-01000-0) from the Korea Research Foundation.
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
