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9 votes
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About Friedrichs historical contribution to QFT cited in Reed and Simon

Friedrichs' early contributions are discussed in On the Stone-von Neumann Uniqueness Theorem and Its Ramifications by S.J. Summers: In the early 1950's, K.O. Friedrichs undertook an influential ...
Carlo Beenakker's user avatar
7 votes
Accepted

Topology on the space of compactly supported functions

The space $C_c(X)$ with the locally convex colimit topology is complete whenever $X$ is paracompact (this confirms the second claim in the comment of @terceira): This is a theorem of Bierstedt proved ...
Jochen Wengenroth's user avatar
5 votes

Let $\phi : A \to B$ be a surjective $*$-homomorphism of star algebras, is there any good notion of "normal bundle of $B$ in $A$"?

Before turning to noncommutative submanifolds in the literature, it's worth remembering that there are three basic approaches for equipping a $\ast$-algebra $A$ with the structure of a 'noncommutative ...
Branimir Ćaćić's user avatar
4 votes
Accepted

Is compact-open topology stable with respect to injective limits?

The answer to your question is certainly negative. Before giving a reference let me spell out what it means that the injection $\injlim L(X,Y_i) \to L(X,\injlim Y_i)$ is an isomorphism onto its range: ...
Jochen Wengenroth's user avatar
4 votes

Convex set with no interior contained in hyperplane?

Here is an example of a convex subset $X$ of an infinite-dimensional separable Hilbert space $H$ with empty interior and which is not contained in any hyperplane of $H$, closed or not. Let $(v_i)_{i\...
Saúl RM's user avatar
  • 10.1k
3 votes

A few points of clarification on the Martin boundary

The Martin kernels are not always harmonic. You need to assume something, for instance that the measure $\mu$ to be finitely supported. In such case, harmonicity is easy to prove : let $y_n$ converge ...
M. Dus's user avatar
  • 1,970
2 votes
Accepted

Is projection of a closed subspace Borel?

It is a Borel set. Indeed, let $P: E \times E \to E$ be projection onto the first coordinate. We need to show $P(D_2) \subset E$ is Borel. $P$, restricted to $D_2$, induces a bounded linear map $Q: ...
David Gao's user avatar
  • 1,332
1 vote

Locally compact groupoid with a Haar system such that the range map restricted to isotropy groupoid is open

In the case of the groupoid G=H⋉X, if the action is free (H⋉X is a principal groupoid), then the range map restricted to isotropy groupoid is open. In general it is not true.
Madalina Buneci's user avatar

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