Timeline for Extending an unbounded dense linear functional
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 14, 2022 at 6:28 | comment | added | Matey Math | OK @YemonChoi your answer is enough for my problem, thank you a lot. | |
| Jan 14, 2022 at 6:19 | comment | added | Yemon Choi | In that case the answer is yes: take a Hamel basis for V and extend it to a Hamel basis for H. Then define your extension of f by setting it to be zero on all the elements of the Hamel basis that do not lie in V. Of course, this is non-constructive and relies on the axiom of choice | |
| Jan 14, 2022 at 6:15 | history | edited | Matey Math | CC BY-SA 4.0 |
added 2 characters in body
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| Jan 14, 2022 at 6:14 | comment | added | Matey Math | @YemonChoi yes $V$ is a dense subspace, sorry now I edit | |
| Jan 14, 2022 at 5:26 | comment | added | Yemon Choi | What do you mean by $f:V\to {\bf C}$ being linear if V is merely a dense subset of H? Are you assuming that V is a dense subspace? | |
| Jan 14, 2022 at 5:12 | history | asked | Matey Math | CC BY-SA 4.0 |