Weyl’s theorem holds for algebraically hyponormal operators
HTML articles powered by AMS MathViewer
- by Young Min Han and Woo Young Lee PDF
- Proc. Amer. Math. Soc. 128 (2000), 2291-2296 Request permission
Abstract:
In this note it is shown that if $T$ is an “algebraically hyponormal" operator, i.e., $p(T)$ is hyponormal for some nonconstant complex polynomial $p$, then for every $f\in H(\sigma (T))$, Weyl’s theorem holds for $f(T)$, where $H(\sigma (T))$ denotes the set of analytic functions on an open neighborhood of $\sigma (T)$.References
- S. K. Berberian, An extension of Weyl’s theorem to a class of not necessarily normal operators, Michigan Math. J. 16 (1969), 273–279. MR 250094, DOI 10.1307/mmj/1029000272
- S. K. Berberian, The Weyl spectrum of an operator, Indiana Univ. Math. J. 20 (1970/71), 529–544. MR 279623, DOI 10.1512/iumj.1970.20.20044
- John B. Conway and Bernard B. Morrel, Roots and logarithms of bounded operators on Hilbert space, J. Funct. Anal. 70 (1987), no. 1, 171–193. MR 870760, DOI 10.1016/0022-1236(87)90129-7
- L. A. Coburn, Weyl’s theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285–288. MR 201969, DOI 10.1307/mmj/1031732778
- Paul Richard Halmos, A Hilbert space problem book, 2nd ed., Encyclopedia of Mathematics and its Applications, vol. 17, Springer-Verlag, New York-Berlin, 1982. MR 675952, DOI 10.1007/978-1-4684-9330-6
- Robin Harte, Fredholm, Weyl and Browder theory, Proc. Roy. Irish Acad. Sect. A 85 (1985), no. 2, 151–176. MR 845539
- Robin Harte, Invertibility and singularity for bounded linear operators, Monographs and Textbooks in Pure and Applied Mathematics, vol. 109, Marcel Dekker, Inc., New York, 1988. MR 920812
- Robin Harte and Woo Young Lee, Another note on Weyl’s theorem, Trans. Amer. Math. Soc. 349 (1997), no. 5, 2115–2124. MR 1407492, DOI 10.1090/S0002-9947-97-01881-3
- Woo Young Lee and Sang Hoon Lee, A spectral mapping theorem for the Weyl spectrum, Glasgow Math. J. 38 (1996), no. 1, 61–64. MR 1373959, DOI 10.1017/S0017089500031268
- Kirti K. Oberai, On the Weyl spectrum. II, Illinois J. Math. 21 (1977), no. 1, 84–90. MR 428073
- Christoph Schmoeger, Ascent, descent and the Atkinson region in Banach algebras. II, Ricerche Mat. 42 (1993), no. 2, 249–264. MR 1283359
- H. Weyl, Über beschränkte quadratische Formen, deren Differenz vollsteig ist, Rend. Circ. Mat. Palermo 27 (1909), 373–392.
Additional Information
- Young Min Han
- Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
- Woo Young Lee
- Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
- MR Author ID: 263789
- Email: wylee@yurim.skku.ac.kr
- Received by editor(s): August 22, 1998
- Published electronically: March 29, 2000
- Additional Notes: This work was partially supported by the BSRI-97-1420 and the KOSEF through the GARC at Seoul National University.
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2291-2296
- MSC (2000): Primary 47A10, 47A53; Secondary 47B20
- DOI: https://doi.org/10.1090/S0002-9939-00-05741-5
- MathSciNet review: 1756089