9
votes

Accepted

### 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 ...

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 ...

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 ...

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: ...

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\...

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 ...

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: ...

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.

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