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Paper
IPM / M / 16536 |
School of Mathematics
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Title: |
Orthogonality preserving pairs of operators on Hilbert C0(Z)-modules
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Author(s): |
Mohammad Bagher Asadi (Joint with F. Olyaninezhad)
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Status: |
Published
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Journal: |
Linear Multilinear Algebra
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Year: |
2020
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Pages: |
DOI: 10.1080/03081087.2020.1825610
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Supported by: |
IPM
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Abstract: |
Suppose that Z is a locally compact Hausdorff space and Ψ,Φ: E→ F are C0(Z) -module maps between
Hilbert C0(Z) -modules such that for every x , y ∈ E, x⊥y implies Ψ(x) ⊥Φ(y). Then there exists a
bounded complex function ϕ on Z that is continuous on
ZE = {z ∈ Z : 〈x , x 〉(z) ≠ 0 for
some x ∈ E } and satisfies
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〈Ψ(x),Φ(y) 〉 = ϕ·〈x , y〉, |
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for all x, y ∈ E .
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