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Results tagged with norms
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user 166628
2
votes
Accepted
Is a mixture of $\ell_p$-norms $\eta(x):=\lVert x\rVert_2 + r\lVert x\rVert_p$ always dimens...
\end{array}
In other words, the norms $\eta$ and $\|\cdot\|_q$ are equivalent on the real vector space $c_{00}$ of finitely supported sequences (i.e. real sequences with only finitely many nonzero terms …
- 1,453
11
votes
Accepted
Subtracting the weak limit reduces the norm in the limit
The property you indicate is known as (strict) Opial’s Property (see https://en.m.wikipedia.org/wiki/Opial_property). It fails generally in reflexive spaces; in fact, it fails generally even for unifo …
- 1,453