All Questions
8 questions with no upvoted or accepted answers
4
votes
0
answers
185
views
A strongly open set which is not measurable in the weak operator topology
Let $H$ be a non-separable Hilbert space and $\{e_i\}_{i\in I}$ be an orthonormal basis for $H$. Let $J$ be a uncountable proper subset in $I$.
Let us put $$E=\{x\in B(H): \lVert xe_j\rVert <1: \...
- 4,058
3
votes
0
answers
225
views
Defining a trace-class operator with a Bochner integral
I had asked this question previously on Math.StacheExchange but did not get an answer there in several months. This isn't strictly speaking research level mathematics but I hope it is sufficiently ...
- 131
2
votes
0
answers
131
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Does a spectral theorem exist for linear operator pencils?
I was wondering if a version of the spectral theorem (the projection valued measure case) holds for linear pencils of the form
$$
A-\lambda B
$$
where $A,B$ are self-adjoint on some Hilbert space $\...
- 223
1
vote
0
answers
133
views
Subspace of RKHS generated by kernel mean embeddings
Suppose $\mathcal{H_k}$ is a reproducing kernel Hilbert space (RKHS) with reproducing kernel $k: \mathcal{X} \times \mathcal{X} \rightarrow \mathbb{R}$. I am looking for results characterising the ...
- 93
1
vote
0
answers
191
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Dual of union of Reproducing Kernel Hilbert Spaces
I have a union of Reproducing Kernel Hilbert Spaces $\mathcal{B}$. I am interested in finding the dual of $\mathcal{B}$. Knowing what the dual is might help to write an alternate formulation for the ...
- 171
1
vote
0
answers
83
views
Embedding random variables in infinite-dimensional spaces
Let $H$ be a reproducing kernel Hilbert space of functions $f:E\to F$ with kernel $k$. A point in $E$ may be embedded into $H$ via the canonical embedding $x\mapsto k(x,\cdot)$. Similarly, a random ...
- 710
0
votes
0
answers
98
views
Does weak $L^2$ approximation implies $L^2$ approximation under a condition similar to convexity?
(Cross posted from Math StackExchange: Does weak $L^2$ approximation implies $L^2$ approximation under a condition similar to convexity?)
Assume $(\Omega, \mu)$ is a probability space. Consider a ...
- 2,830
0
votes
0
answers
107
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Norm equivalences for Gaussian random functions (Cameron-Martin space)
Preliminaries
Consider the Hilbert space $H :={L^2_{\text{per}}(\mathbb{R})}$ of Gaussian random functions, $2\pi$-periodic in $\mathbb{R}$.
These random functions are drawn from a Gaussian measure $\...
- 101