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Semi-Fredholm operators and pure contractions in Hilbert space

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Abstract

In Kaufman (Proc Amer Math Soc 72: 531–534, 1978) proved that the function \(\Gamma \) defined by \(\Gamma (A)=A(I-A^{*}A)^{-1/2}\) maps the set \(\fancyscript{C}_{0}(H)\) of all pure contractions one-to-one onto the set \(\fancyscript{C}(H)\) of all closed and densely defined linear operators on Hilbert space \(H\). In this paper, we gives some further properties of \(\Gamma \), we establish the semi-Fredholmness and Fredholmness of unbounded operators in terms of bounded pure contractions, and we apply this results to an 2 \(\times \) 2 upper triangular operator matrices. An application to linear delay differential equation is given.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, ENSET d’Oran, BP 1523, El M’naouar, Oran, Algeria

    Mohammed Benharrat

  2. Department of Mathematics, University of Oran, BP 1524, El M’naouar, Oran, Algeria

    Bekkai Messirdi

Authors
  1. Mohammed Benharrat
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  2. Bekkai Messirdi
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Correspondence to Mohammed Benharrat.

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Benharrat, M., Messirdi, B. Semi-Fredholm operators and pure contractions in Hilbert space. Rend. Circ. Mat. Palermo 62, 267–272 (2013). https://doi.org/10.1007/s12215-013-0123-9

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  • DOI: https://doi.org/10.1007/s12215-013-0123-9

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