Timeline for Regarding basis of holomorphic Hardy space
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 29, 2022 at 15:33 | comment | added | Yemon Choi | But if you replace the word "maximal" in your comment with the property "has dense linear span" then yes, I think that should work. | |
| Jun 29, 2022 at 15:32 | comment | added | Yemon Choi | I think that arguing via maximality in an incomplete inner product space can be a bit risky. If you consider C[-1,1] with the usual (L^2) inner product and then define V to be the set of all f in C[-1,1] such that $\int_{-1}^0 f = \int_0^1 f$ then one can show that no non-zero vector in C[-1,1] is orthogonal to all of V. Hence, if $(u_n)$ is an ONB of $V$ then it is a maximal orthonormal set in C[-1,1] but it does not span C[-1,1] | |
| Jun 29, 2022 at 14:05 | comment | added | Naruto | So, basically, by Zorns lemma and Gram-Schmidt orthogonalization process, I can obtain a maximal sequence ${u_{n}}$ in an inner product space $A^{\infty}(\Omega).$ and then, as what you said, it follows. | |
| Jun 29, 2022 at 13:57 | vote | accept | Naruto | ||
| Jun 24, 2022 at 15:19 | history | edited | Yemon Choi | CC BY-SA 4.0 |
added details in response to request in comments.
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| Jun 24, 2022 at 13:42 | comment | added | Naruto | Can you provide some more details? | |
| Jun 15, 2022 at 22:29 | history | answered | Yemon Choi | CC BY-SA 4.0 |