# Questions tagged [hilbert-spaces]

For questions involving Hilbert spaces, that is, complete normed spaces whose norm comes from an inner product.

4,951 questions
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### BLP in terms of a Hilbert space

I am reading Stein's 2013 monograph 'Interpolation of Spatial Data' where he characterizes the best linear predictor (BLP) in terms of a Hilbert space. Let $Q$ be the set on which a random process $Z$...
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### Uniform convergence of polynomial approximation on Schwartz space

I have a question regarding uniform convergence of basis expansion in Schwartz space. For $L^2(\mathbb{R},\lambda)$, $\lambda$ Lebesgue measure, the partial sums of basis expansion (Hermite functions) ...
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### Is there any theory in physics that can be modelled in any type of space (Hilbert space, Euclidean, Non-Euclidean…etc)? [on hold]

And if yes, could that theory also contain/be compatible with all types of (physical) symmetries?
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### Is there a norm making $C([0,1])$ into a Hilbert space?

The space $C([0,1])$ of continuous functions on $[0,1]$ is an inner product space under the $L^2$-norm, but not complete. Equipped instead with the $L^\infty$-norm, it becomes complete but the norm is ...
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### Product of two Linear Operators

Let $S(e_n)=e_{n+1}$ and $T(e_n)=e_{n+2}$ be two linear operators on the Hilbert space $l_2(N)$, the space of all sequences $\sum_{1}^\infty |a_k|^2 < \infty$, and $\{e_n\}, n=0,1,2,...$ is the ...
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### Are these two norms on the dual space of a Hilbert space equivalent?

Let $\mathcal{H}$ be a Hilbert space, and $\mathcal{H}^*$ its topological dual space (the space of continuous linear forms on $\mathcal{H}$). The exists a conjugate-linear isometry between these two ...
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### Convergence of trace class operators in Hilbert Schmidt norm

Let $\mathscr{A}_n$ be a sequence of trace-class operators on a Hilbert space $\mathcal{H}$ and let further $\mathscr{A}$ be another trace-class operator on the same space. Assume that $\mathscr{A}_n$...
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### General Formula of a Linear Operator given its act on the Standard Orthonormal Basis

I am trying to find a general formula for a linear operator on a Hilbert space when its action on the standard orthonormal basis is known. I include my work below. Please tell me whether my solution ...
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### Finding Adjoint Linear Operators in a Hilbert Space

I am looking for verification of my attempt in finding the adjoint operator of a linear operator. Let $S(e_n)=e_{2n+1}$ be a linear operator in the Hilbert space $l^2(N)$, the space of all summable ...
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