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1 results

  • Parareductive Operators on Banach Spaces

  • Roman Drnovšek
  • Journal:
    Canadian Mathematical Bulletin / Volume 37 / Issue 3 / 01 September 1994
    Published online by Cambridge University Press:
    20 November 2018, pp. 346-350
    Print publication:
    01 September 1994
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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.