Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the Helton class of -hyponormal operators


Authors: Yoenha Kim, Eungil Ko and Ji Eun Lee
Journal: Proc. Amer. Math. Soc. 135 (2007), 2113-2120
MSC (2000): Primary 47B20; Secondary 47A10
DOI: https://doi.org/10.1090/S0002-9939-07-08708-4
Published electronically: February 28, 2007
MathSciNet review: 2299488
Full-text PDF Free Access

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 $ p$-hyponormal operators has a nontrivial invariant subspace if its spectrum has its interior in the plane.


References [Enhancements On Off] (What's this?)

  • 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 $ 0 < p < 1$, 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 $ x$ 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 $ p$-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: https://doi.org/10.1090/S0002-9939-07-08708-4
Received by editor(s): December 14, 2004
Received by editor(s) in revised form: March 13, 2006
Published electronically: 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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society