Geodesic
Parareductive Operators on Banach Spaces
Canadian mathematical bulletin, Tome 37 (1994) no. 3, pp. 346-350

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DOI

This note gives a Banach space extension of the Hilbert space result due to P. A. Fillmore (see [3]). In particular, it is shown that the adjoint T* = A — iB of an operator T = A + iB (with A and B hermitian) is a polynomial in T if and only if T* leaves invariant every linear subspace invariant under T, and this is equivalent to the assertion that T* leaves invariant every paraclosed subspace invariant under T.
DOI : 10.4153/CMB-1994-051-1
Mots-clés : 47A15, 47B15, invariant subspaces, hermitian and normal operators on Banach spaces 
Drnovšek, Roman. Parareductive Operators on Banach Spaces. Canadian mathematical bulletin, Tome 37 (1994) no. 3, pp. 346-350. doi: 10.4153/CMB-1994-051-1
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     title = {Parareductive {Operators} on {Banach} {Spaces}},
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     year = {1994},
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