# Tagged Questions

341 views

### Which Sigma-Ideals in a Sigma-Algebra are Ideals of Null Sets?

My question is motivated, to be somewhat vague, by an attempt to see how much a measure space is defined by the set of null sets. In other words, assume we are not given a concrete measure on a space ...
384 views

### When does a $W^*$-algebra have a standard Borel spectrum?

EDIT: AndrĂ© Henriques has commented below that the correct separability condition is not weak-* separability as I have written below, but separability of the predual. This post came out a bit long, ...
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### definition of operator valued integral with spectral measure

I am trying to make sense of some operators that come up on Buchholz and Summers' work on warped convolutions (two works on arxiv: 2008 and 2011). There, they work on a Hilbert space $H$ and on the ...
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### Do semi-continuous functions generate bounded Borel measurable functions as a $C^*$-algebra?

This question is related to Question 2 of my previous posting. Question. Let $\mu$ be a Radon measure on a compact Hausdorff space $\Omega$ and $L^{\infty}(\Omega,\mu)$ the set of essentially bounded ...
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### Is there an inclusion of $L_\infty(G)$ into $C_0(G)^{**}$?

This is probably a silly question with which I am stuck however. Let $G$ be a locally compact group. It seems to me that there is a canonical map of $L_\infty(G)$ into $M=C_0(G)^{**}$ (the latter is ...
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### Nonseparable disintegration theory: references

I mean a theorem of the following kind. Let $A$ be a C*-algebra, and let $\pi: A\to B(H)$ be its representation. Then there exist a set $P$ with a positive measure $\mu$, a field of Hilbert spaces ...
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### What kind of completion is this?

Let $X$ be a compact Hausdorff space, and $C(X)$ the unital commutative C*-algebra of continuous functions on it. The double Banach dual $C(X)^{**}$ is a commutative von Neumann algebra and hence has ...
Hi, I came across the statement below and I couldn't figure out why it is true. I was hoping someone could explain it or give me a good reference. Thank you in advance. "Let $\pi$ be a non-degenerate ...