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  • LINEAR ORTHOGONALITY PRESERVERS OF HILBERT BUNDLES

  • Part of
  • CHI-WAI LEUNG, CHI-KEUNG NG, NGAI-CHING WONG
  • Journal:
    Journal of the Australian Mathematical Society / Volume 89 / Issue 2 / October 2010
    Published online by Cambridge University Press:
    05 November 2010, pp. 245-254
    Print publication:
    October 2010
    • Article
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  • A ℂ-linear map θ (not necessarily bounded) between two Hilbert C*-modules is said to be ‘orthogonality preserving’ if 〈θ(x),θ(y)〉=0 whenever 〈x,y〉=0. We prove that if θ is an orthogonality preserving map from a full Hilbert C0(Ω)-module E into another Hilbert C0(Ω) -module F that satisfies a weaker notion of C0 (Ω) -linearity (called ‘localness’), then θ is bounded and there exists ϕ∈Cb (Ω)+ such that 〈θ(x),θ(y)〉=ϕ⋅〈x,y〉 for all x,y∈E.