Linear Orthogonality Preservers of Hilbert Bundles
نویسندگان
چکیده
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()-module E into another Hilbert C0()-module F that satisfies a weaker notion of C0()-linearity (called ‘localness’), then θ is bounded and there exists φ ∈ Cb()+ such that 〈θ(x), θ(y)〉 = φ · 〈x, y〉 for all x, y ∈ E . 2010 Mathematics subject classification: primary 46L08; secondary 46M20, 46H40, 46E40.
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