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Proceedings of the American Mathematical Society

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A geometric equivalent of the invariant subspace problem


Authors: Eric A. Nordgren, Heydar Radjavi and Peter Rosenthal
Journal: Proc. Amer. Math. Soc. 61 (1976), 66-68
MSC: Primary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1976-0430822-9
MathSciNet review: 0430822
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Abstract: It is shown that every operator has an invariant subspace if and only if every pair of idempotents has a common invariant subspace.


References [Enhancements On Off] (What's this?)

  • [1] Chandler Davis, Generators of the ring of bounded operators, Proc. Amer. Math. Soc. 6 (1955), 970-972. MR 17, 389. MR 0073138 (17:389a)
  • [2] Paul R. Halmos, Normal dilations and extensions of operators, Summa Brasil. Math. 2 (1950), 125-134. MR 13, 359. MR 0044036 (13:359b)
  • [3] Heydar Radjavi and Peter Rosenthal, Invariant subspaces, Springer-Verlag, New York, 1973. MR 51 #3924. MR 0367682 (51:3924)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0430822-9
Keywords: Bounded linear operator, invariant subspace
Article copyright: © Copyright 1976 American Mathematical Society

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