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Nov 17, 2018 at 0:55 comment added Nate Eldredge The second paragraph is also a proof all by itself, since the weak-* topology on $X^*$ is not metrizable, so it cannot embed in any metrizable space.
Apr 27, 2018 at 9:27 history edited Jochen Wengenroth CC BY-SA 3.0
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Apr 27, 2018 at 6:03 comment added ABB @ Tomek Kania Probably it works: the product on $B(X)$ is jointly norm continuous but this point is not valid concerning SOT.
Apr 26, 2018 at 16:47 comment added Tomasz Kania Is there an easy argument to see that the SOT topology is different from the norm topology on a general Banach space without using, for example, the Josefson-Nissenzweig theorem?
Apr 26, 2018 at 16:29 vote accept ABB
Apr 26, 2018 at 14:33 history edited Jochen Wengenroth CC BY-SA 3.0
corrected spelling
Apr 26, 2018 at 13:44 history answered Jochen Wengenroth CC BY-SA 3.0