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Results tagged with norms
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user 61785
10
votes
Accepted
Banach space with uncountable basis
I will pull together the comments into a community wiki answer with some of my own remarks so that the question isn't left on the unanswered questions list.
If you're willing to accept that it is cons …
5
votes
Accepted
Sequence in *-algebra with different limits for two C*-norms?
Then
$$
\|a_i\|_1 = \|a_i-b\|_1 \leq \|a_i - b\|_2 \to 0
$$
So $(a_i)_i$ is convergent with respect to both norms and has limit $0$ in $\|\cdot\|_1$, but its limit in $\|\cdot\|_2$ is $b \neq 0$. …
- 3,768