×

zbMATH — the first resource for mathematics

Browder-type theorems and SVEP. (English) Zbl 1241.47008
Summary: We study the new properties \((b)\) and \((gb)\), which we had introduced in [M. Berkani and H. Zariouh, Math. Bohem. 134, No. 4, 369–378 (2009; Zbl 1211.47011)], for an operator having the SVEP on the complement of distinguished parts of its spectrum. Classes of operators are considered as illustrating examples.

MSC:
47A53 (Semi-) Fredholm operators; index theories
47A10 Spectrum, resolvent
47A11 Local spectral properties of linear operators
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] P. Aiena, Fredholm and Local Spectral Theory, with Applications to Multipliers, Kluwer Academic Publishers, (2004). · Zbl 1077.47001
[2] Aiena P., Miller T.L.: On generalized a-Browder’s theorem. Stud. Math. 180(3), 285–300 (2007) · Zbl 1119.47002 · doi:10.4064/sm180-3-7
[3] Aiena P., Peña P.: Variations on Weyl’s theorem. J. Math. Anal. Appl. 324, 566–579 (2006) · Zbl 1101.47001 · doi:10.1016/j.jmaa.2005.11.027
[4] Amouch M., Berkani M.: On the property (gw). Mediterr. J. Math. 5(3), 371–378 (2008) · Zbl 1188.47011 · doi:10.1007/s00009-008-0156-z
[5] Amouch M., Zguitti H.: On the equivalence of Browder’s and generalized Browder’s theorem. Glasgow Math. J. 48, 179–185 (2006) · Zbl 1097.47012 · doi:10.1017/S0017089505002971
[6] Arora S.C., Arora P.: On p-quasihyponormal operators for 0 < p < 1. Yokohama Math. J. 41, 25–29 (1993) · Zbl 0792.47026
[7] Berkani M.: On the equivalence of Weyl theorem and generalized Weyl theorem. Acta Mathematica sinica, English series 23(1), 103–110 (2007) · Zbl 1116.47015 · doi:10.1007/s10114-005-0720-4
[8] Berkani M.: B-Weyl spectrum and poles of the resolvent. J. Math. Anal. Applications 272(2), 596–603 (2002) · Zbl 1043.47004 · doi:10.1016/S0022-247X(02)00179-8
[9] Berkani M., Sarih M.: On semi B-Fredholm operators. Glasgow Math. J. 43, 457–465 (2001) · Zbl 0995.47008
[10] M. Berkani and N. Castro and S. V. Djordjević, Single valued extension property and generalized Weyl’s theorem, Mathematica Bohemica, 131 (2006), No. 1, p. 29-38. · Zbl 1114.47015
[11] M. Berkani and A. Arroud, B-Fredholm and spectral properties for multipliers in Banach algebras, Rend. Circ. Math. Palermo, Serie II, Tomo LV (2006), 385–397. · Zbl 1123.47031
[12] Berkani M., Koliha J.J.: Weyl type theorems for bounded linear operators. Acta Sci. Math. (Szeged) 69, 359–376 (2003) · Zbl 1050.47014
[13] Berkani M., Zariouh H.: Extended Weyl type theorems. Mathematica Bohemica 134, 4 369–378 (2009) · Zbl 1211.47011
[14] Coburn L.A.: Weyl’s theorem for nonnormal operators. Michigan Math. J. 13, 285–288 (1966) · Zbl 0173.42904 · doi:10.1307/mmj/1031732778
[15] Duggal B.P., Jeon I.H., Kim I.H.: On Weyl’s theorem for quasi-class A operators. J. Kor. Math. Soc. 43, 899–909 (2006) · Zbl 1133.47009 · doi:10.4134/JKMS.2006.43.4.899
[16] T. Furuta; M. Ito and T. Yamazaki, A subclass of paranormal operators including class of log-hyponormal and several related classes, Sci. Math. 1 (1998) p. 389–403. · Zbl 0936.47009
[17] Laursen K.B., Neumann M.M.: An Introduction to Local Spectral Theory. Clarendon, Oxford (2000) · Zbl 0957.47004
[18] Rakočević V.: Operators obeying a-Weyl’s theorem. Rev. Roumaine Math. Pures Appl. 34, 915–919 (1989) · Zbl 0686.47005
[19] Rakočević V.: On a class of operators. Mat. Vesnik. 37, 423–426 (1985) · Zbl 0596.47001
[20] A. L. Shields, Weighted shift operators and analytic function theory, in: C. Pearcy (Ed.), Topics in operator theory, in: Math. Survey, vol. 105, Amer. Math. Soc., Providence, RI, 1974, pp. 49–128. · Zbl 0303.47021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.