# Tag Info

## Hot answers tagged operator-norms

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### What is the $L^p$-norm of the (uncentered) Hardy-Littlewood maximal function?

Those are basic yet difficult questions. I don't know much about the uncentered case, but here is some information on the centered case. A nonempty set $B \subseteq \mathbb{R}^d$ is centrally ...
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### Norm of $n$-linear symmetric forms

After a bit of searching, I found that $\gamma_n=1$ for all $n$. This is known as "van der Corput-Schaake inequality" (1935), discovered before by Szegö (1928), and mentioned to have been known to ...
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### which norms can be realized as operator norms?

Here is a non trivial constraint : ${\rm Hom}(V,W)$ contains (is spanned by) rank one morphisms $$v\mapsto\ell(v)w,\qquad\ell\in V',w\in W.$$ If a given norm over ${\rm Hom}(V,W)$ is induced, then \|...
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### Characterizing when matrices are 'dissipative'

The discrete-time analogue -- there exists a norm in which $|A_1^nx|\leq |x|$, $|A_2^nx|\leq |x|$ for all $n\geq 1$ and $x \in\mathbb{R}^d$ -- is equivalent to the property that the semigroup ...
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### Bounding the matrix norm of a commutator $[A,B]$ in terms of the norms of $A$ and $B$
Concerning your first question, as I noted in my comment above for any operator norm we have $\Vert [A,B]\Vert \leq 2\Vert A\Vert\Vert B\Vert$. Conversely, let $A = \pmatrix{1 & 0 \\ 0 & -1}$,...
Though two answers are already posted, let me explain how to understand that it is false from general reasoning. The inequality $\|(I+A+B)^{-1}A\|\leqslant 1$ is equivalent to \$\|(I+A+B)^{-1}A x\|\...