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Nov 6, 2020 at 17:39 comment added Martin Väth This is exactly the situation which I have described (in case $\beta=0$ and equality of the norms): Unfortunately, exactly in this case it is not possible to conclude that the operator is closed, because $A\in B(X,Y)$ is an empty requirement then.
Nov 6, 2020 at 8:54 comment added Jarek Sarnowski $X$ and $Y$ indeed have different norm. What if, additionally, norm on $X$ is equivalent to the norm $||(\beta I - A)y||_{Y}$?
Nov 6, 2020 at 6:26 vote accept Jarek Sarnowski
Nov 6, 2020 at 5:15 history edited Martin Väth CC BY-SA 4.0
Fix typo
Nov 6, 2020 at 5:08 history answered Martin Väth CC BY-SA 4.0