On invariant linear manifolds
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- by P. A. Fillmore
- Proc. Amer. Math. Soc. 41 (1973), 501-505
- DOI: https://doi.org/10.1090/S0002-9939-1973-0338804-X
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Abstract:
For a linear transformation $A$ on a Banach space, let $\mathcal {L}(A)$ be the lattice of (not necessarily closed) invariant subspaces of $A$. For $A$ bounded it is shown that if $\mathcal {L}(A \oplus A) \subset \mathcal {L}(T \oplus T)$, or if $\mathcal {L}(A) \subset \mathcal {L}(T)$ and $T$ commutes with $A$, then $T$ is a polynomial in $A$. In the case of a Hilbert space, if $\mathcal {L}(A) \subset \mathcal {L}({A^ \ast })$ then ${A^ \ast }$ is a polynomial in $A$.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 501-505
- MSC: Primary 47A15
- DOI: https://doi.org/10.1090/S0002-9939-1973-0338804-X
- MathSciNet review: 0338804