query: Why is an $n$th power a norm in a Kummer extension?
positive_passages.docid: 151910
positive_passages.text: Why is $K^{\ast n}$ contained in the norm group?
negative_passages.docid: 9159
negative_passages.text: $L^p$-norm of a non-negative measurable function
negative_passages.docid: 155621
negative_passages.text: Finiteness of the dimension of a normed space and compactness
negative_passages.docid: 145535
negative_passages.text: Product norm on infinite product space
negative_passages.docid: 50160
negative_passages.text: The quotient norm on $\ell^{\infty}(\mathbb{N}) / c_0 (\mathbb{N})$ is given by $\limsup_{n \in \mathbb{N}} |x_n|$.
negative_passages.docid: 157455
negative_passages.text: Show that the norm of the multiplication operator $M_f$ on $L^2[0,1]$ is $\|f\|_\infty$
negative_passages.docid: 105170
negative_passages.text: About product of $k$ commutators
negative_passages.docid: 149536
negative_passages.text: Why is the  $L_p$ norm strictly convex for $1<p<\infty?$
negative_passages.docid: 67625
negative_passages.text: $C([0, 1])$ is not complete with respect to the norm $\lVert f\rVert _1 = \int_0^1 \lvert f (x) \rvert \,dx$
negative_passages.docid: 118564
negative_passages.text: Dual cone of a $L^1$ norm cone?
negative_passages.docid: 73254
negative_passages.text: spectral radius in normed space is subadditive.
negative_passages.docid: 81240
negative_passages.text: Norm of an inverse operator: $\|T^{-1}\|=\|T\|^{-1}$?
negative_passages.docid: 149664
negative_passages.text: Norm is sup of inner products (proof).
negative_passages.docid: 34272
negative_passages.text: Proving definition of norms induced by vector norms
negative_passages.docid: 89555
negative_passages.text: Inequality for the p norm of a convolution
negative_passages.docid: 128361
negative_passages.text: The kernel and range of the powers of a self-adjoint operator
negative_passages.docid: 81112
negative_passages.text: Proving that the dual of the $\mathcal{l}_p$ norm is the $\mathcal{l}_q$ norm.