Background Consider a real Banach$^1$ space $V$. We'll call a subset $V_+ \subseteq V$ a cone if $V$ is closed, $\alpha V_+ \subseteq V_+$ for every $\alpha \geqslant 0$ and $V_ …

Suppose that $X$ is a Banach space (or more generally, Frechet space) such that $X$ is the closure of the span of a compact (in the original topology) subset $K$. Do we know anythi …

(Note that I am interested in the Gelfand-Pettis integral specifically, as opposed to, for example, the Bochner integral.) I have tried Googling things like "integral topological …

Let $E$ be a reflexive Banach space and let $B(E)$ be the space of bounded operators on $E$ endowed with the weak operator topology. In particular, the unit ball of $B(E)$ is then …

Let $F$ be a finite degree extension over $\mathbf{Q}_p$ and consider the locally profinite group $G:=GL_2(\mathbf{Q}_p)$. P1: Give an interesting example (non-artificial one, i. …

In the short biography article on the Alexander Grothedieck http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf , it is mentioned that after Grothendieck submitting his …

Consider (abstract) von Neumann algebras topologised by their weak*-topology arising from the unique predual. In the theory of topological vector spaces, there is a natural notion …

I am interested in operators on a non-reflexive Banach space. Let $X$ be a Banach space and let $L(X)$ be the algebra of operators acting on $X$. We may embed $L(X)$ into $L(X^{\as …

(Assume Countable Choice.) Generalizing arxiv.org/pdf/math/9903103 and www.um.es/beca/papers/BirkhoffBourgain.pdf, the Riemann-Lebesgue integral can be defined as follows: For $ …

On Bourbaki's TVS Chapter IV pages 33-34, the last part of Proposition 2 can be formulated as follows: Notations: $K$ - The underlying field which is the real or complex number f …

Let $M$ be a manifold equipped with a pair of surjective submersions $N_1 \stackrel{p_1}{\leftarrow} M \stackrel{p_2}{\rightarrow} N_2$ where $dim N_1 = dim N_2 = n$. Then we can f …

Dear All, I'm reading a paper (Residuality of Dynamical Morphisms by Burton, Keane and Serafin) that makes a claim that I've been unable to verify or find a reference for. The cla …

After reviewing the (locally convex) topological vector spaces that I know, the only examples I could find where there is an isomorphism from the space to its (anti)dual, are Hil …

What is an example of a non-paracompact topological vector space? I'm aware of this question, but I don't care if my tvs is locally convex. In fact the wilder the better. The only …

Part 1: How big is the category $TVS_{loc.conv.}$ of locally convex topological vector spaces (and continuous maps)? In other words (and less cheekily), is there a free locally c …