Timeline for Question on operator topologies convergence
Current License: CC BY-SA 4.0
11 events
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| Sep 26, 2019 at 17:52 | comment | added | Jesse Peterson | It might be worth pointing out that if $H$ is separable then the SOT-topology is metrizable when you restrict to norm bounded subsets. | |
| Sep 25, 2019 at 7:44 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Sep 25, 2019 at 7:07 | history | edited | javi1996 | CC BY-SA 4.0 |
edited body
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| Sep 24, 2019 at 14:30 | history | edited | javi1996 | CC BY-SA 4.0 |
added 63 characters in body
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| Sep 24, 2019 at 14:16 | comment | added | javi1996 | Yes, but I'm not including the hypothesis of being *-subalgebras, just only a subalgebra. | |
| Sep 24, 2019 at 14:13 | comment | added | Yemon Choi | So just to try and pin down a precise question: you are asking if there is an infinite-dimensional $*$-subalgebra of ${\mathcal B}(\ell_2)$ in which every SOT-convergent sequence is automatically norm-convergent? | |
| Sep 24, 2019 at 14:07 | comment | added | javi1996 | Yes, that what I mean. It is easy to see that it cannot happen in the whole algebra, but are there any infinite-dimensional subalgebras with this property? | |
| Sep 24, 2019 at 13:46 | comment | added | Yemon Choi | What do you mean by asking for two topologies to "coincide sequentially"? Are you asking if every sequence that converges in SOT automatically converges in norm? Because if so, a simple counterexample is given by taking $P_n\in {\mathcal B}(\ell_2)$ to be the orthogonal projection onto the span of the $n$th standard basis vector; we have $P_n\to 0$ in SOT while $\Vert P_n\Vert=1$ for all $n$ | |
| Sep 24, 2019 at 13:33 | history | edited | Ivan Izmestiev | CC BY-SA 4.0 |
typos corrected, grammar slightly modified
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| Sep 24, 2019 at 13:30 | review | First posts | |||
| Sep 24, 2019 at 13:44 | |||||
| Sep 24, 2019 at 13:28 | history | asked | javi1996 | CC BY-SA 4.0 |