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Stability Theorems for Linear Combinations of Idempotents

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Abstract.

We prove a stability theorem for the nullity of a linear combination c 1 P 1 + c 2 P 2 of two idempotent operators P 1, P 2 on a Banach space provided c 1, c 2 and c 1 + c 2 are nonzero. We then show that for c 1 P 1 + c 2 P 2 the property of being upper semi-Fredholm, lower semi-Fredholm and Fredholm, respectively, is independent of the choice of c 1, c 2, and that the nullity, defect and index of c 1 P 1 + c 2 P 2 are stable.

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Authors and Affiliations

  1. Department of Mathematics, University of Melbourne, Melbourne, VIC, 3010, Australia

    J. J. Koliha & V. Rakočević

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  1. J. J. Koliha
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  2. V. Rakočević
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Correspondence to J. J. Koliha.

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Koliha, J.J., Rakočević, V. Stability Theorems for Linear Combinations of Idempotents. Integr. equ. oper. theory 58, 597–601 (2007). https://doi.org/10.1007/s00020-007-1495-z

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  • DOI: https://doi.org/10.1007/s00020-007-1495-z

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