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Three-space theorem for semi-Fredholmness

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Abstract

A three-space theorem for upper semi-Fredholmness (resp. lower semi-Fredholmness) is proved.

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References

  1. Ambrozie C.-G., Vasilescu F.-H.: Banach space complexes. Kluwer Academic Publishers, Dordrecht-Boston-London (1995)

    Book  MATH  Google Scholar 

  2. Barnes B.A.: Restrictions of bounded linear operators: closed range, Proc. Amer. Math. Soc. 135, 1735–1740 (2007)

    Article  MATH  Google Scholar 

  3. Barnes B.A.: Spectral and Fredholm theory involving the diagonal of a bounded linear operator, Acta Sci. Math. (Szeged) 73, 237–250 (2007)

    MATH  Google Scholar 

  4. Caradus S.R., Pfaffenberger W.E., Yood B.: Calkin algebras and algebras of operators on Banach spaces. Marcel Dekker, New York (1974)

    MATH  Google Scholar 

  5. Castillo J.M.F., González M.: Three-space problems in Banach space theory. Springer-Verlag, Berlin-Heidelberg-New York (1997)

    MATH  Google Scholar 

  6. Djordjević S.V., Duggal B.P.: Spectral properties of linear operator through invariant subspaces, Funct. Anal. Approx. Comput. 1, 19–29 (2009)

    Google Scholar 

  7. Djordjević S.V., Duggal B.P.: Drazin invertibility of the diagonal of an operator. Linear Multilinear Algebra 60, 65–71 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fang X.: Samuel multiplicity and the structure of semi-Fredholm operators, Adv. Math. 186, 411–437 (2004)

    MATH  Google Scholar 

  9. Grabiner S.: Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34, 317–337 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  10. Grabiner S., Zemánek J.: Ascent, descent, and ergodic properties of linear operators, J. Operator Theory 48, 69–82 (2002)

    MathSciNet  MATH  Google Scholar 

  11. Harte R.: Invertibility and singularity for bounded linear operators. Marcel Dekker, New York (1988)

    MATH  Google Scholar 

  12. Laursen, K.B., Neumann, M.M. An Introduction to Local Spectral Theory. Oxford University Press, 2000.

  13. A. E. Taylor and D. C. Lay, Introduction to functional analysis, 2nd Edition, John Wiley and Sons, New York-Chichester-Brisbane-Toronto, 1980.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, People’s Republic of China

    Qingping Zeng & Huaijie Zhong

Authors
  1. Qingping Zeng
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  2. Huaijie Zhong
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Corresponding author

Correspondence to Qingping Zeng.

Additional information

This work has been supported by the National Natural Science Foundation of China (11171066), Specialized Research Fund for the Doctoral Program of Higher Education (20103503110001, 20113503120003), Natural Science Foundation of Fujian Province (2011J05002, 2012J05003), and the Foundation of the Education Department of the Fujian Province (JB10042).

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Zeng, Q., Zhong, H. Three-space theorem for semi-Fredholmness. Arch. Math. 100, 55–61 (2013). https://doi.org/10.1007/s00013-012-0471-2

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  • DOI: https://doi.org/10.1007/s00013-012-0471-2

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