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Parareductive Operators on Banach Spaces

  • Roman Drnovšek (a1)

Abstract

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.

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References

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1. Bonsall, F. F and Duncan, J., Numerical Ranges of Operators on Normed Spaces and of Elements of Nor me d Algebras, London Math. Soc. Lecture Note Ser. 2, Cambridge University Press, 1971.
2. Dowson, H. R., Spectral Theory of Linear Operators, London Math. Soc. Monographs 12, Academic Press, London, 1978.
3. Fillmore, P. A., A Note on Reductive Operators, Canad. Math. Bull. 22(1979), 101102.
4. Fillmore, P. A., On Invariant Linear Manifolds, Proc. Amer. Math. Soc. 41(1973), 501505.
5. Omladic, M., Parareflexive Operators on Banach Spaces, Michigan Math. J. 37(1990), 133143.
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Parareductive Operators on Banach Spaces

  • Roman Drnovšek (a1)

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