A sufficient condition for hyperinvariance
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- by W. E. Longstaff PDF
- Proc. Amer. Math. Soc. 61 (1976), 26-28 Request permission
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.References
- L. Brickman and P. A. Fillmore, The invariant subspace lattice of a linear transformation, Canadian J. Math. 19 (1967), 810–822. MR 213378, DOI 10.4153/CJM-1967-075-4
- R. G. Douglas and Carl Pearcy, On a topology for invariant subspaces, J. Functional Analysis 2 (1968), 323–341. MR 0233224, DOI 10.1016/0022-1236(68)90010-4
- Peter Rosenthal, A note on unicellular operators, Proc. Amer. Math. Soc. 19 (1968), 505–506. MR 222703, DOI 10.1090/S0002-9939-1968-0222703-6
- Donald Sarason, The $H^{p}$ spaces of an annulus, Mem. Amer. Math. Soc. 56 (1965), 78. MR 188824
Additional Information
- © Copyright 1976 American Mathematical Society
- 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