Generalisation: isomorphism of sequences spaces

Asked Feb 05 '19 at 11:02

Active Feb 05 '19 at 11:02

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As is well known, the isometric isomorphism $(c_0)^* \cong \ell^1$ holds.

Is there an analogous statement for general $L^p$ spaces?

Perhaps a good start would be to wonder about generalizations of sequence spaces like $c_0, c_{00}, c, \dots$. Is is sensible to think of those as special cases of functions converging to $0$ and functions with compact support?

asked Feb 05 '19 at 11:02

Qi Zhu

9,413

https://en.wikipedia.org/wiki/Lp_space#Dual_spaces Maybe you are looking for that. – Nathanael Skrepek Feb 05 '19 at 11:10
https://www.math.ksu.edu/~nagy/real-an/4-06-dual-lp.pdf – Peter Melech Feb 05 '19 at 11:13
I'm afraid that's not what I'm looking for. Isometries for dual spaces of $L^p$ spaces are generally well known (possibly what I'm asking for is so as well - we have not covered it in the lecture, though and I have not yet found anything on the internet/in literature) - what I ask in my question is different. – Qi Zhu Feb 05 '19 at 11:19
2

You may find this interesting. – Julián Aguirre Feb 05 '19 at 11:40
That's perfect - thank you. – Qi Zhu Feb 05 '19 at 20:46

Generalisation: isomorphism of sequences spaces

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