Additive Maps Preserving Nilpotent Perturbation of Scalars View Full Text


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Article Info

DATE

2019-03

AUTHORS

Ting Zhang, Jin Chuan Hou

ABSTRACT

Let X be a Banach space over F(=RorC) with dimension greater than 2. Let N(X) be the set of all nilpotent operators and B0(X) the set spanned by N(X). We give a structure result to the additive maps on FI+B0(X) that preserve rank-1 perturbation of scalars in both directions. Based on it, a characterization of surjective additive maps on FI+B0(X) that preserve nilpotent perturbation of scalars in both directions are obtained. Such a map Φ has the form either Φ(T) = cAT A−1 +ϕ(T)I for all T∈FI+B0(X) or Φ(T) = cAT* A−1 + ϕ(T)I for all T∈FI+B0(X), where c is a nonzero scalar, A is a τ-linear bijective transformation for some automorphism τ of F and ϕ is an additive functional. In addition, if dim X = ∞, then A is in fact a linear or conjugate linear invertible bounded operator. More... »

PAGES

1-20

References to SciGraph publications

  • 2005-10. Additive Maps Preserving Nilpotent Operators or Spectral Radius in ACTA MATHEMATICA SINICA, ENGLISH SERIES
  • Journal

    TITLE

    Acta Mathematica Sinica, English Series

    ISSUE

    N/A

    VOLUME

    N/A

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    URI

    http://scigraph.springernature.com/pub.10.1007/s10114-018-8048-z

    DOI

    http://dx.doi.org/10.1007/s10114-018-8048-z

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