WEYL'S THEOREM FOR CLASS A(k) OPERATORS

MARY, J. STELLA IRENE ; PANAYAPPAN, S.

Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 39-46

Résumé

In this paper we shall show that Weyl's theorem holds for class A(k) operators T where k≥>1, via its hyponormal transform . Next we shall prove some applications of Weyl's theorem on class A(k) operators.

Détail

DOI : 10.1017/S0017089507003904

Mots-clés : 47A13, 47A63

Bibliographie

[1] 1.Aiena, P. and Carpintero, C., Weyl's theorem, α- Weyl's theorem and single valued extension property, Extracta Math. 20 (2005), 25–41. Google Scholar

[2] 2.Aluthge, A., Some generalised theorems on p-hyponormal operators, Int. Eq. 0p. Th. 24 (1996), 497–501. Google Scholar | DOI

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

[4] 4.Cho, M., Itoh, M. and Oshiro, S., Weyl's theorem holds for p-hyponormal operators, Glasgow Math. J. 39 (1997), 217–220. Google Scholar | DOI

[5] 5.Cho, M. and Yamazaki, T., An operator transform from class A to the class of hyponormal operators and its application, Int. Eq. 0p. Th. 53 (2005), 497–508. Google Scholar | DOI

[6] 6.Chourasia, N. N. and Ramanujan, P. B., Paranormal operators on Banach space, Bull. Austral. Math. Soc. 21 (1980), 161–168. Google Scholar | DOI

[7] 7.Coburn, L. A., Weyl's theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285–288. Google Scholar | DOI

[8] 8.Curto, R. E. and Han, Y. M., Weyl's theorem, a-Weyl's theorem and local spectral theory, J. London Math. Soc. (2) 67 (2003), 499–509. Google Scholar | DOI

[9] 9.Curto, R. E. and Han, Y. M., Weyl's theorem for algebraically paranormal operators, Int. Eq. 0p. Th. 47 (2003), 307–314. Google Scholar | DOI

[10] 10.Duggal, B. P. and Kubrusly, C., Weyl's theorems for posinormal operators, J. Korean. Math. Soc. 42 (2005), 529–541. Google Scholar | DOI

[11] 11.Duggal, B. P., Jeon, I. H. and Kim, I. H., On Weyl's theorem for quasi-class A operators, J. Korean. Math. Soc. 43 (2006), 899–909. Google Scholar | DOI

[12] 12.Fujii, M., Jung, D., Lee, S. H., Lee, M. Y. and Nakamoto, Some class of operators related to paranormal and log-hyponormal operators, Math. Japan. 51 (2000), 395–402. Google Scholar

[13] 13.Furuta, T., Ito, M. and Yamazaki, T., A subclass of paranormal operators including class of log-hyponormal and several related classes, Sci. Math. 1 (1998), 389–403. Google Scholar

[14] 14.Han, Y. M. and Lee, W. Y., Weyl's theorem holds for algebraically hyponormal operators Proc. Amer. Math. Soc. 128 (2000), 2291–2296. Google Scholar | DOI

[15] 15.Han, Y. M. and Lee, W. Y., Weyl spectra and Weyl's theorem, Studia Math. 148 (2001), 193–206. Google Scholar | DOI

[16] 16.Hansen, F., An inequality, Math. Ann. 246 (1980), 249–250. Google Scholar | DOI

[17] 17.Ito, M. and Yamazaki, T., Relations between two inequalities and and their applications, Int. Eq. Op. Th. 44 (2002), 442–450. Google Scholar | DOI

[18] 18.Mary, J. S. I. and Panayappan, S., Some properties of class A(k) operators and their hyponormal transforms, Glasgow Math. J. 49 (2007), 133–143. Google Scholar | DOI

[19] 19.Mechrei, S., Weyl's theorem for algebraically class A operators, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 239–246.

[20] 20.Stampfli, J., Hyponormal operators, Pacific J. Math. 12 (1962), 1453–1458. Google Scholar | DOI

[21] 21.Uchiyama, A., Weyl's theorem for class A operators, Math.Inequal. Appl. 4 (2001), 143–150.

[22] 22.Yamazaki, T., On powers of class A(k) operators including p-hyponormal and log hyponormal operators, Math. Inequal. Appl. 3 (2000), 97–104. Google Scholar