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Fredholm Properties of the Difference of Orthogonal Projections in a Hilbert Space

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Abstract.

Buckholtz (Proc. Amer. Math. Soc. 128 (2000), 1415–1418) gave necessary and sufficient conditions for the invertibility of the difference of two orthogonal projections in a Hilbert space. We generalize this result by investigating when the difference of such projections is a Fredholm operator, and give an explicit formula for its Fredholm inverse.

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Authors and Affiliations

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

    J. J. Koliha

  2. Faculty of Science and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia–Montenegro

    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. Fredholm Properties of the Difference of Orthogonal Projections in a Hilbert Space. Integr. equ. oper. theory 52, 125–134 (2005). https://doi.org/10.1007/s00020-003-1274-4

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  • DOI: https://doi.org/10.1007/s00020-003-1274-4

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