A remark on a paper of J. S. Ruan: “Invariant subspace of strictly singular operators” [Proc. Amer. Math. Soc. 108 (1990), no. 4, 931–936; MR1002160 (90g:47009)]

Fitzpatrick, Patrick M.; Goldberg, Seymour

doi:10.1090/S0002-9939-1991-1062386-1

Proceedings of the American Mathematical Society

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

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A remark on a paper of J. S. Ruan: “Invariant subspace of strictly singular operators” [Proc. Amer. Math. Soc. 108 (1990), no. 4, 931–936; MR1002160 (90g:47009)]
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by Patrick M. Fitzpatrick and Seymour Goldberg PDF

Proc. Amer. Math. Soc. 112 (1991), 601 Request permission

Abstract:

We observe that a strictly singular operator is not necessarily condensing, so that the invariant subspace problem for strictly singular operators remains open.

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