Questions tagged [hilbert-spaces]
A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.
258 questions with no upvoted or accepted answers
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Bounded operators with infinite matrix representations
I asked this question on StackExchange originally, but I'm giving it a go here as well.
Suppose that $A$ is a unital $C^*$-algebra, $\varphi\colon A\to B(H)$ is a unital, completely positive map and ...
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Speed of convergence of vector expansions in non orthogonal basis
Suppose we have a finite-norm vector $X$ in a Hilbert space, and we want to construct its expansion in a certain (infinite) basis $V_k$, $X=\sum_k a_k V_k$. If the basis is orthonormal, then we know ...
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"correlation" between two subspaces
It is frequently important to determine the coherence of a matrix by finding the maximum pairwise correlation between all its column vectors. Similarly, when working with a union of subspaces of a ...
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separable spaces-QM vs. functional analysis
In Nouredine Zettili's QM book, Hilbert space $H$ is said to be separable when: There exists a Cauchy sequence $\psi_n \in H$ ($n=1,2,\ldots)$ such that for every $\psi$ of $H$ and $\varepsilon > 0,...
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Is $GL_{S^1}(H)$ (for $H$ Hilbert space ) path-connected?
Due to the negative answer to my last question I want to know if at least the following is true:
Let H be an infinite dimensional separable complex Hilbert space with $S^1$-action. Let $\text{Gl}_{S^...
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General form of a symplectic map
A symplectic automorphism of a Hilbert space has the form $T=U(\cosh S+J\sinh S)$ for a unitary $U$, an antilinear involution $J$ and a positive operator $S$. In fact a version of this goes through in ...
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how take weak derivative of norms in hilbert spaces?
Let the following be hilbert spaces with dens inclusions $V ↪H=H^* ↪V^*$. Where $H^*$ and $V^*$ are the duals. $H$ has the product $(*,*)$ and $V×V^*$ has the product $⟨*,*⟩$.
Let $u∈L^2 ([0,T];V); ...
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Determine the singular values of a compact operator in terms of the eigenvalues of an alternating tensor product of operators
Let $H$ be a $\mathbb R$-Hilbert space, $A\in\mathfrak L(H)$ be compact and $$|A|:=\sqrt{A^\ast A}$$ denote the square-root of $A$. By definition, the $k$th largest singular value $\sigma_k(A)$ of $A$ ...
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