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Proceedings of the American Mathematical Society

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Compact operators with root vectors that span


Authors: D. Deckard, C. Foiaş and C. Pearcy
Journal: Proc. Amer. Math. Soc. 76 (1979), 101-106
MSC: Primary 47B05
DOI: https://doi.org/10.1090/S0002-9939-1979-0534397-8
MathSciNet review: 534397
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Abstract: A concrete example is given of a bounded, linear, compact, quasiaffinity T acting on a separable, infinite dimensional, Hilbert space $ \mathcal{H}$ with the property that the eigenvectors of T span $ \mathcal{H}$ but the root vectors of $ {T^ \ast }$ span a subspace of $ \mathcal{H}$ with infinite dimensional orthocomplement.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0534397-8
Keywords: Compact, quasiaffinity, root vector
Article copyright: © Copyright 1979 American Mathematical Society