Timeline for What are the major differences between real and complex Banach space?
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| Dec 3, 2016 at 21:46 | comment | added | anonymous | While the general Bishop–Phelps theorem is false for complex Banach spaces, it is worth noting that it holds for complex Banach space X with the Radon–Nikodym property. | |
| Nov 27, 2016 at 7:14 | history | edited | KConrad | CC BY-SA 3.0 |
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| Nov 27, 2016 at 7:09 | comment | added | Ice sea | @AmirSagiv You are right. But for the parabolic systems, like activator-Inhibitor model, semi-conduct model, Belousov–Zhabotinskii models and so on, the field should be the real field. The common way to deal with the problem is as follows: First we extend it the complex field, and then show that the solution is actually real if the initial value is real and the coefficients are real. | |
| Nov 27, 2016 at 6:21 | comment | added | Amir Sagiv | To throw in my two cents about the last statement - even classical electrodynamics are complex by nature. Therefore, the treatment of optical waves in the Helmholz and Schrodinger (linear and nonlinear) equations is complex by nature. | |
| Nov 26, 2016 at 16:54 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |