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On the localized weak Bishop’s property

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Abstract

This note is devoted to a weaker version of Bishop property \(\beta\) at a given complex number. We show in particular that this notion is a regularity and hence the induced spectrum satisfies all classical properties of the spectrum.

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References

  1. Aiena, P., Müller, V.: The localized single-valued extension property and Riesz operators. Proc. Am. Math. Soc. 143, 2051–2055 (2015)

    Article  MathSciNet  Google Scholar 

  2. Albrecht, E., Eschmeier, J., Neumann, M.M.: Some topics in the theory of decomposable operators. In: Douglas, R.G., Pearcy, C.M., Sz.-Nagy, B., Vasilescu, FH., Voiculescu, D., Arsene, G. (eds.) Advances in Invariant Subspaces and Other Results of Operator Theory: Advances and Applications, vol. 17, pp. 15–34. Birkhäuser, Basel (1986)

    Chapter  Google Scholar 

  3. Benhida, C., Zerouali, E.H.: Local spectral theory of linear operators RS and SR. Integral Equ. Oper. Theory 54, 1–8 (2006)

    Article  MathSciNet  Google Scholar 

  4. Boucekkine, E.: Bishop’s Condition and Related Properties in Local Spectral Analysis Of Operators. Diss. Carleton University (1994)

  5. Bourhim, A., Miller, V.G.: The single-valued extension property is not preserved under sums and products of commuting operators. Glasg. Math. J. 49, 99–104 (2007)

    Article  MathSciNet  Google Scholar 

  6. Kordula, V., Müller, V.: On the axiomatic theory of spectrum. Stud. Math. 119, 109–128 (1996)

    MathSciNet  MATH  Google Scholar 

  7. Laursen, K.B., Neumann, M.M.: An Introduction to Local Spectral Theory. Clarendon Press, Oxford Science Publications, Oxford (2000)

    MATH  Google Scholar 

  8. Mbekhta, M., Müller, V.: On the axiomatic theory of spectrum II. Stud. Math. 119, 129–147 (1996)

    Article  MathSciNet  Google Scholar 

  9. Müller, V.: Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, 2nd edn. Birkhäuser, Berlin (2007)

    MATH  Google Scholar 

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Acknowledgements

The authors are dept full for the anonymous referee for valuable comments that improved the first version of this paper.

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Authors and Affiliations

  1. Département de Mathématiques et Informatique, Faculté des Sciences, Université Ibn Tofail, Kénitra, Morocco

    Bouazza El Wahbi

  2. Centre de préparation à l’agrégation des Mathématiques, CRMEF Rabat-Salé-Kénitra, Rabat, Morocco

    Haddou Khachane & Belkassem Seddoug

  3. Centre de recherches mathématiques de Rabat, Faculté des Sciences, Université Mohammed V-Agdal, B.P. 1014, Rabat, Morocco

    El Hassan Zerouali

Authors
  1. Bouazza El Wahbi
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  2. Haddou Khachane
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  3. Belkassem Seddoug
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  4. El Hassan Zerouali
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Corresponding author

Correspondence to El Hassan Zerouali.

Additional information

Communicated by Anton Baranov.

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El Wahbi, B., Khachane, H., Seddoug, B. et al. On the localized weak Bishop’s property. Ann. Funct. Anal. 11, 970–980 (2020). https://doi.org/10.1007/s43034-020-00063-z

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  • DOI: https://doi.org/10.1007/s43034-020-00063-z

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