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A sufficient condition for hyperinvariance


Author: W. E. Longstaff
Journal: Proc. Amer. Math. Soc. 61 (1976), 26-28
MSC: Primary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1976-0430820-5
MathSciNet review: 0430820
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Abstract: A linear transformation on a finite-dimensional complex linear space has the property that all of its invariant subspaces are hyperinvariant if and only if its lattice of invariant subspaces is distributive [1]. It is shown that an operator on a complex Hilbert space has this property if its lattice of invariant subspaces satisfies a certain distributivity condition.


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  • [1] L. Brickman and P. A. Fillmore, The invariant subspace lattice of a linear transformation, Canad. J. Math. 19(1967), 810-822. MR 35 #4242. MR 0213378 (35:4242)
  • [2] R. G. Douglas and Carl Pearcy, On a topology for invariant subspaces, J. Functional Analysis 2(1968), 323-341. MR 38 #1547. MR 0233224 (38:1547)
  • [3] Peter Rosenthal, A note on unicellular operators, Proc. Amer. Math. Soc. 19(1968), 505-506. MR 36 #5753. MR 0222703 (36:5753)
  • [4] Donald Sarason, The $ {H^p}$ spaces of an annulus, Mem. Amer. Math. Soc. No. 56(1965). MR 32 #6256. MR 0188824 (32:6256)

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DOI: https://doi.org/10.1090/S0002-9939-1976-0430820-5
Article copyright: © Copyright 1976 American Mathematical Society

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