Timeline for What are the major differences between real and complex Banach space?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 31, 2017 at 1:38 | comment | added | Henry.L | I am now kind of curious what kind of methods are available when dealing with complex valued optimization problems? Can you point some reference? Thank you very much! :) | |
| May 30, 2017 at 20:06 | comment | added | gerw | I think you can use $L^p(0,1)$ and the functional $x \mapsto \|x\|_{L^p(0,1)}^p$, with $p > 1$. | |
| May 30, 2017 at 20:04 | comment | added | Henry.L | I mean, what if we consider your claim in a Banach, yet not Hilbert space as the OP asked. | |
| May 30, 2017 at 20:03 | comment | added | gerw | Yes, but it should hold for all kind of derivatives. | |
| May 30, 2017 at 20:02 | comment | added | Henry.L | You said that "the range of the derivative has to be $\mathbb{R}$", you specifically mean Frechet derivative right? Can you provide a counter example in real Banach space? In Hilbert space your claim is plain. | |
| May 30, 2017 at 19:59 | comment | added | gerw | No, I do not have a reference, but the proof is short and easy. I do not understand your second question. | |
| May 30, 2017 at 17:09 | comment | added | Henry.L | Any reference for this claim? And I think you mean that Frechet derivative has to be real, right? | |
| Dec 3, 2016 at 18:49 | history | answered | gerw | CC BY-SA 3.0 |