Abstract
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 direction 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.
Original language | English |
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Article number | 124744 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 495 |
Issue number | 2 |
DOIs | |
Publication status | Accepted/In press - 2020 |
Keywords
- (Modular) Birkhoff-James orthogonality
- Continuous function
- Locally compact Hausdorff space
- Non-linear isomorphism