Timeline for Characterize this subspace of the bounded operators on $ L^2(\mathbb{R}) $
Current License: CC BY-SA 4.0
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| Jan 27, 2022 at 13:25 | comment | added | Nik Weaver | BTW, as Onur Oktay points out, you have described a CCR algebra (over the symplectic space $\mathbb{C}$ with symplectic form $\{a,b\} = {\rm Im}(a\bar{b})$). It is known that these algebras are always simple (noted in the above link), so that's another reason they can't contain any compact operators. Otherwise the intersection with the compacts would be a nontrivial ideal. | |
| Jan 26, 2022 at 3:32 | history | edited | Nik Weaver | CC BY-SA 4.0 |
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| Jan 25, 2022 at 14:53 | vote | accept | Ian Gershon Teixeira | ||
| Jan 25, 2022 at 11:35 | history | edited | Nik Weaver | CC BY-SA 4.0 |
edited body
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| Jan 25, 2022 at 4:39 | history | answered | Nik Weaver | CC BY-SA 4.0 |