Timeline for Cartesian product of Banach spaces: all norms such that the inclusion is an isometry are equivalent?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 14, 2020 at 9:39 | comment | added | Philip Brooker | @NikWeaver: I seem to recall that I discovered it by accident, when trawling through Eve Oja's papers on Zentralblatt Math as a graduate student. I made a mental note of it at the time ("the norm on a direct sum need not be 'like' a direct sum of norms"), but haven't used it since - until now! | |
| Apr 14, 2020 at 9:34 | history | edited | Philip Brooker | CC BY-SA 4.0 |
I added a note to my answer acknowledging Bill Johnson's counterexample in the comments
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| Apr 14, 2020 at 9:29 | comment | added | Philip Brooker | @BillJohnson: thanks, Bill! That's a nice, simple way of stating a counterexample; I'd had a specific such counterexample in mind (i.e., of quasi-complemented, non-complemented subspaces of $\ell_2$), but hadn't thought about it in such general terms. | |
| Apr 11, 2020 at 18:25 | comment | added | Bill Johnson | Take $H$, $K$ to be quasi-complementary, non complementary subspaces of a Hilbert space $J$ and norm $H \oplus K$ with $\|(x,y)\| := \|x+y\|_J$. | |
| Apr 11, 2020 at 13:08 | comment | added | Nik Weaver | Wow! I didn't know this! | |
| Apr 11, 2020 at 13:06 | history | edited | Philip Brooker | CC BY-SA 4.0 |
Provided some details of the additional hypothesis and fixed some typos
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| Apr 11, 2020 at 12:03 | history | answered | Philip Brooker | CC BY-SA 4.0 |