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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Inverses généralisés d’opérateurs non bornés
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by J.-Ph. Labrousse PDF
Proc. Amer. Math. Soc. 115 (1992), 125-129 Request permission

Abstract:

This paper is devoted to the definition and the study of the generalized inverses of unbounded densely defined closed operators in Banach and Hubert spaces. In this latter case an identity is established that links the orthogonal projection on the graph of an operator to the orthogonal projection on the graph of its Moore-Penrose inverse.
References
  • H. O. Cordes and J. P. Labrousse, The invariance of the index in the metric space of closed operators, J. Math. Mech. 12 (1963), 693–719. MR 0162142, DOI 10.1017/s0022112062000440
  • Jean-Philippe Labrousse, Les opérateurs quasi Fredholm: une généralisation des opérateurs semi Fredholm, Rend. Circ. Mat. Palermo (2) 29 (1980), no. 2, 161–258 (French, with English summary). MR 636072, DOI 10.1007/BF02849344
  • J-Ph. Labrousse and M. M’Bekhta, Les opérateurs points de continuité pour la conorme et l’inverse de Moore-Penrose (à paraître).
  • M. Zuhair Nashed (ed.), Generalized inverses and applications, University of Wisconsin, Mathematics Research Center, Publication No. 32, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0451661
  • M. H. Stone, On unbounded operators in Hilbert space, J. Indian Math. Soc. (N.S.) 15 (1951), 155–192 (1952). MR 52042
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 115 (1992), 125-129
  • MSC: Primary 47A05
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1079701-6
  • MathSciNet review: 1079701