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Fredholmness of Linear Combinations of Two Idempotents

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Abstract.

Let E and F be idempotent operators on a complex Hilbert space, and let a and b be nonzero scalars with a + b ≠ 0. We prove that aE + bF is Fredholm if and only if E + F is, thus answering affirmatively a question asked by Koliha and Rakočević.

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Authors and Affiliations

  1. Department of Mathematics, National Central University, Chungli, 320, Taiwan

    Hwa-Long Gau

  2. Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 300, Taiwan

    Pei Yuan Wu

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  1. Hwa-Long Gau
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  2. Pei Yuan Wu
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Correspondence to Pei Yuan Wu.

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Gau, HL., Wu, P.Y. Fredholmness of Linear Combinations of Two Idempotents. Integr. equ. oper. theory 59, 579–583 (2007). https://doi.org/10.1007/s00020-007-1531-z

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  • DOI: https://doi.org/10.1007/s00020-007-1531-z

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