Timeline for The product of two controlled operators is also a controlled operator

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Apr 26, 2018 at 12:36	comment	added	Paul Siegel		If so then you just have to take the definition, which gives necessary and sufficient conditions for $x$ to be in $Supp(v)$, and rewrite it so that it gives necessary and sufficient conditions for $x$ to not be in $Supp(v)$. That's what I wrote in my answer.
Apr 26, 2018 at 12:35	comment	added	Paul Siegel		@C.Ding Without having my copy of the book in front of me, I assume that the $\mathfrak{C}$ you're referring to is the family of localizing sets in the definition of "geometric hilbert space over $X$". I assume that "We choose a decomposition $X = \bigcup X_j$ as in Definition 4.20" also refers to the localizing sets, so the $X_j$'s are interchangeable with the $B$'s.
Apr 26, 2018 at 6:05	comment	added	C. Ding		The support of $ v\in H $ is the set of points $x\in X$ such that for every $B\in \mathfrak C$ that contains $x$, $\lambda(B)v\neq 0$. I really can't see why $x\notin \operatorname{Supp}(v)$ implies there is a $X_j$ containing $x$ such that $\lambda(X_j)v=0$. This is in fact what I want to ask.
Apr 26, 2018 at 1:20	history	answered	Paul Siegel	CC BY-SA 3.0