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# Questions tagged [operator-norms]

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### In the proof of Neural Tangent Kernel stays constant in infinite width limit, why the norm of the dual mapping operator equals operator norm of kernel

For a fixed distribution $p^{in}$ on the input space $\mathbb{R}^{n_0}$, consider a function space $\mathcal{F}$ defined as $\{{f: \mathbb{R}^{n_0} \rightarrow \mathbb{R}^{n_L}}\}$. On this space, ...
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### Existence of more than two C*-norms on algebraic tensor product of C*-algebras

Let $A$ and $B$ be two C*-algebras. Then $(A,B)$ is called is a nuclear pair if there is a unique $C^*$-norm on the algebraic tensor product $A\odot B$. If $A$ or $B$ is nuclear, then all pairs $(A,B)$...
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### Tail bound on largest singular value of Gaussian Wigner matrix

I have problem on deducing the following tail bound on largest singular value of Gaussian Wigner matrix $\|W\|\leq(2+\epsilon)\sqrt{n}$, $\forall\epsilon$, with high probability. There is a hint: see ...
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1 vote
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### How to prove that $\|A^tv\|_2 \leq \|Av\|_2^t$ for every $0<t<1$? [closed]

Consider a unit norm $\|V\|_2=1$ and a symmetric matrix $A$. I wish to prove that $\|A^tv\|_2 \leq \|Av\|_2^t$ for every $0<t<1$. My belief is that this is true is motivated by empirical ...
353 views

### Trace norm of operators obtained by restricting the matrix of a trace class operator

Suppose $H$ is a Hilbert space with orthonormal basis $\{e_i\}_{i\in \mathbb N}$. To every operator $T$, we associate a infinite matrix $[T_{ij}]$, where $T_{ij}=\left<Te_j,e_i\right>$. We know ...
1 vote
52 views

### Row-wise conjugation of completely bounded map by group action

Let $B$ be a $G$-$C^*$-algebra and let $\phi\colon B \to B$ be a completely bounded map (not necessarily $G$-equivariant). For group elements $F := \{h_1, \ldots, h_k\} \subset G$ we consider the ...
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The Schur norm of a matrix $A$ is defined to be $\|A\|_S=\max\{\|A\circ X\|: \|X\|\leq 1\}$, where $\|\cdot \|$ is the operator norm of a matrix, i.e., the largest singular value. Let $a_1,\ldots, ... 0 votes 1 answer 171 views ### Does$\{\left|\varphi\right>\left<\psi\right|+\left|\psi\right>\left<\varphi\right||\varphi\in\{\psi\}^{\perp}\}$split$\mathfrak{S}_1$? Let$\mathfrak{S}_1$be the space of trace-class self-adjoint operators on$L^2(\mathbb{R}^n)$, and$\psi\in L^2(\mathbb{R}^n)$such that$\int |\psi|^2 = 1$. Is there a projection from$\mathfrak{S}... 