Timeline for Interpolation of embedded Hilbert spaces and intersection
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 7, 2021 at 19:13 | comment | added | rebo79 | @MikaeldelaSalle I edited the post with the definition given by Triebel, and indeed is what you mean. At the very end in my particular case $\mathcal{H}_2$ is not closed in $\mathcal{H}_1$ (is a dense subspace instead), so I cannot expect that $P$ is still continuous when restricted to $\mathcal{H}_2$. I'm grateful with your remarks, thanks! | |
| Feb 7, 2021 at 19:08 | history | edited | rebo79 | CC BY-SA 4.0 |
added 225 characters in body
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| Feb 7, 2021 at 13:38 | comment | added | Mikael de la Salle | Yes, that us what meant by compatible, and (I Guess) what Triebel means by $L(\{A0,A1\},\{A0,A1\})$. Note however that the projections need not be orthogonal. | |
| Feb 6, 2021 at 23:06 | comment | added | rebo79 | Thinking about it, you mean that if $P: \mathcal{H}_1\to \mathcal{H}_1\cap X$ is the (linear continuous) projector, then $P$ when restricted to $\mathcal{H}_2$ is the (linear continuous) projector to $\mathcal{H}_2\cap X$, right? | |
| Feb 6, 2021 at 22:47 | comment | added | rebo79 | @MikaeldelaSalle Sorry, but what do you mean by compatible projections? Although "compatible" is a widely used concept, I don't know it in this context and google doesn't seem to help me. Thanks! | |
| Feb 6, 2021 at 22:20 | comment | added | Mikael de la Salle | I think that what your are missing is that you need that $H_1 \cap X$ and $H_2 \cap X$ are complemented subspaces of $H_1$ and $H_2$ with compatible projections. | |
| Feb 6, 2021 at 21:08 | history | edited | rebo79 |
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| Feb 6, 2021 at 9:42 | review | First posts | |||
| Feb 6, 2021 at 9:48 | |||||
| Feb 6, 2021 at 9:35 | history | asked | rebo79 | CC BY-SA 4.0 |