A note on the a -Browder’s and a -Weyl’s theorems

M. Amouch; H. Zguitti

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 2, page 157-166
  • ISSN: 0862-7959

Abstract

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Let T be a Banach space operator. In this paper we characterize a -Browder’s theorem for T by the localized single valued extension property. Also, we characterize a -Weyl’s theorem under the condition E a ( T ) = π a ( T ) , where E a ( T ) is the set of all eigenvalues of T which are isolated in the approximate point spectrum and π a ( T ) is the set of all left poles of T . Some applications are also given.

How to cite

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Amouch, M., and Zguitti, H.. "A note on the $a$-Browder’s and $a$-Weyl’s theorems." Mathematica Bohemica 133.2 (2008): 157-166. <http://eudml.org/doc/250520>.

@article{Amouch2008,
abstract = {Let $T$ be a Banach space operator. In this paper we characterize $a$-Browder’s theorem for $T$ by the localized single valued extension property. Also, we characterize $a$-Weyl’s theorem under the condition $E^a(T)=\pi ^a(T),$ where $E^a(T)$ is the set of all eigenvalues of $T$ which are isolated in the approximate point spectrum and $\pi ^a(T)$ is the set of all left poles of $T.$ Some applications are also given.},
author = {Amouch, M., Zguitti, H.},
journal = {Mathematica Bohemica},
keywords = {B-Fredholm operator; Weyl’s theorem; Browder’s thoerem; operator of Kato type; single-valued extension property; B-Fredholm operator; Weyl's theorem; operator of Kato type; single-valued extension property (SVEP)},
language = {eng},
number = {2},
pages = {157-166},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on the $a$-Browder’s and $a$-Weyl’s theorems},
url = {http://eudml.org/doc/250520},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Amouch, M.
AU - Zguitti, H.
TI - A note on the $a$-Browder’s and $a$-Weyl’s theorems
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 2
SP - 157
EP - 166
AB - Let $T$ be a Banach space operator. In this paper we characterize $a$-Browder’s theorem for $T$ by the localized single valued extension property. Also, we characterize $a$-Weyl’s theorem under the condition $E^a(T)=\pi ^a(T),$ where $E^a(T)$ is the set of all eigenvalues of $T$ which are isolated in the approximate point spectrum and $\pi ^a(T)$ is the set of all left poles of $T.$ Some applications are also given.
LA - eng
KW - B-Fredholm operator; Weyl’s theorem; Browder’s thoerem; operator of Kato type; single-valued extension property; B-Fredholm operator; Weyl's theorem; operator of Kato type; single-valued extension property (SVEP)
UR - http://eudml.org/doc/250520
ER -

References

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  1. Fredholm Theory and Local Spectral Theory, with Applications to Multipliers, Kluwer Academic Publishers, 2004. (2004) MR2070395
  2. Operators which do not have the single valued extension property, J. Math. Anal. Appl. 250 (2000), 435–448. (2000) MR1786074
  3. Weyl type theorems for operators satisfying the single-valued extension property, J. Math. Anal. Appl. 326 (2007), 1476–1484. (2007) Zbl1117.47007MR2280999
  4. Generalized a -Weyl’s theorem and the single-valued extension property, Extracta. Math. 21 (2006), 51–65. (2006) Zbl1123.47005MR2258341
  5. On the equivalence of Browder’s and generalized Browder’s theorem, Glasgow Math. J. 48 (2006), 179–185. (2006) MR2224938
  6. Single valued extension property and generalized Weyl’s theorem, Math. Bohem. 131 (2006), 29–38. (2006) MR2211001
  7. Generalized Weyl’s theorem and hyponormal operators, J. Aust. Math. Soc. 76 (2004), 291–302. (2004) MR2041251
  8. Weyl type theorems for bounded linear operators, Acta Sci. Math. (Szeged) 69 (2003), 359–376. (2003) MR1991673
  9. On semi B-Fredholm operators, Glasgow Math. J. 43 (2001), 457–465. (2001) MR1878588
  10. Browder’s theorems and spectral continuity, Glasgow Math. J. 42 (2000), 479–486. (2000) MR1793814
  11. Hereditarily normaloid operators, Extracta Math. 20 (2005), 203–217. (2005) Zbl1160.47301MR2195202
  12. The single valued extension property on a Banach space, Pacific J. Math. 58 (1975), 61–69. (1975) Zbl0315.47002MR0374985
  13. Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34 (1982), 317–337. (1982) Zbl0477.47013MR0651274
  14. Weyl’s theorem holds for algebraically hyponormal operators, Proc. Amer. Math. Soc. 128 (2000), 2291–2296. (2000) MR1756089
  15. A note on a -Weyl’s theorem, J. Math. Anal. Appl. 260 (2001), 200–213. (2001) MR1843976
  16. Isolated spectral points, Proc. Amer. Math. Soc. 124 (1996), 3417–3424. (1996) Zbl0864.46028MR1342031
  17. Operators with finite ascent, Pacific. Math. J. 152 (1992), 323–336. (1992) Zbl0783.47028MR1141799
  18. An Introduction to Local Spectral Theory, Clarendon, Oxford, 2000. (2000) MR1747914
  19. Spectral analysis using ascent, descent, nullity and defect, Math. Ann. 184 (1970), 197–214. (1970) Zbl0177.17102MR0259644
  20. Généralisation de la décomposition de Kato aux opérateurs paranormaux et spectraux, Glasgow Math. J. 29 (1987), 159–175. (1987) Zbl0657.47038MR0901662
  21. Résolvant généralisé et théorie spectrale, J. Operator Theory 21 (1989), 69–105. (1989) Zbl0694.47002MR1002122
  22. On the axiomatic theory of the spectrum II, Studia Math. 119 (1996), 129–147. (1996) MR1391472
  23. Weyl’s and Browder’s theorem for operators satisfying the SVEP, Studia Math. 163 (2004), 85–101. (2004) 
  24. On the essential approximate point spectrum II, Mat. Vesnik 36 (1984), 89–97. (1984) MR0880647
  25. Approximate point spectrum and commuting compact perturbations, Glasgow Math. J. 28 (1986), 193–198. (1986) MR0848425
  26. Operators obeying a -Weyl’s theorem, Rev. Roumaine Math. Pures Appl. 34 (1989), 915–919. (1989) MR1030982
  27. Über beschränkte quadratische Formen, deren Differenz vollstetig ist, Rend. Circ. Mat. Palermo 27 (1909), 373–392. (1909) 
  28. A note on generalized Weyl’s theorem, J. Math. Anal. Appl. 324 (2006), 992–1005. (2006) Zbl1101.47002MR2201769

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