Non-linear modular Birkhoff-James orthogonality preservers between spaces of continuous functions (Q1995890)
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scientific article; zbMATH DE number 7315634
| Language | Label | Description | Also known as |
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| English | Non-linear modular Birkhoff-James orthogonality preservers between spaces of continuous functions |
scientific article; zbMATH DE number 7315634 |
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Non-linear modular Birkhoff-James orthogonality preservers between spaces of continuous functions (English)
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25 February 2021
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A new notion of non-linear isomorphisms between Banach modules is introduced based on modular Birkhoff-James orthogonality. It is shown that a (possibly non-linear) bijective modular Birkhoff-James orthogonality preserver in both directions between spaces of continuous functions (vanishing at infinity) induces a homeomorphism between underlying locally compact Hausdorff spaces. Moreover, characterizations of linear and additive modular Birkhoff-James orthogonality preservers between spaces of continuous functions are also given in terms of the induced homeomorphisms and continuous functions having constant absolute values.
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(modular) Birkhoff-James orthogonality
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continuous function
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locally compact Hausdorff space
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nonlinear isomorphism
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