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Parareductive Operators on Banach Spaces

Published online by Cambridge University Press:  20 November 2018

Roman Drnovšek
Roman Drnovšek*
Affiliation:
Institute of Mathematics, Physics and Mechanics Jadranska 19 61111 Ljubljana Slovenia e-mail:, Roman.Drnovsek@uni-Ij.ac.mail.si
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Abstract

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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.

Keywords

47A1547B15invariant subspaceshermitian and normal operators on Banach spaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 3 , 01 September 1994 , pp. 346 - 350
Copyright
Copyright © Canadian Mathematical Society 1994

References

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.Google Scholar
2. Dowson, H. R., Spectral Theory of Linear Operators, London Math. Soc. Monographs 12, Academic Press, London, 1978.Google Scholar
3. Fillmore, P. A., A Note on Reductive Operators, Canad. Math. Bull. 22(1979), 101–102.Google Scholar
4. Fillmore, P. A., On Invariant Linear Manifolds, Proc. Amer. Math. Soc. 41(1973), 501–505.Google Scholar
5. Omladic, M., Parareflexive Operators on Banach Spaces, Michigan Math. J. 37(1990), 133–143.Google Scholar