All Questions

Let $X$ be a set. Over the Banach fields $F=\mathbb{R}$ or $F=\mathbb{C}$ we can define the Banach space$$\ell^2(X)=\{\xi\colon X\to F\mid \sum_{x\in X}|\xi(x)|^2<\infty\}$$which satisfies a list ...

There have been several works characterizing weak topology by nonstandard analysis, which give rise to the following monad ($X$ is a Hilbert space): $$\mu(0) = \{y\in{}^{*}X: \forall x\in X ~~ \...

For what kind of topological vector spaces (separable maybe?) are the closed convex subsets countable intersections of halfspaces. I've seen somewhere that it's true for separable Hilbert spaces, ...

I already posted my question on mathstackexchange For a separable Hilbert space $H$ it is known that the unitary group $U(H)$ is contractible, both for the norm topology (Kuiper's theorem) and for ...

I have few questions about the subsets of a normed space $X$ endowed with the weak topology. Let $E$ be such subset. When is the norm a continuous function on $E$? When is the metric induced by the ...

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 Hilbert spaces. So my ...