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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

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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