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Results tagged with operator-norms
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user 763
6
votes
Accepted
Finding a norm on $ \mathbb{R}^X $ such that the "natural" embedding of a metric space $ X $...
Note that your embedding map $T$ actually takes values in the subspace
$\newcommand{\R}{{\mathbb R}}$
$c_{00}(X;\R)$ of finitely supported functions $X\to\R$. If you merely want a norm on this subspa …
- 25.8k
7
votes
Accepted
Is the matrix induced L1-norm greater than the induced L2-norm?
To avoid ambiguity I will write $\lVert\cdot\rVert_{p\to r}$ for the $\ell_p$-to-$\ell_r$-norm. Note that in general, $\lVert A\rVert_{1\to r} = \max_{1\leq j\leq n} \lVert (Ae_j)\rVert_r$.
Let $A$ be …
- 25.8k
4
votes
Accepted
$M_Λ(A) → A ⊗ M_Λ(C)$
The norm on $M_\Lambda(A)$ is the one obtained by identifying it as a vector space (not an algebra) with $\ell^1(\Lambda\times\Lambda, A)$.
Similarly, the norm on $M_\Lambda({\mathbb C})$ is the one …
- 25.8k