# Questions tagged [topological-vector-spaces]

A topological vector space is a vector space $V$ over a topological field $\mathbb{K}$ (typically $\mathbb{K}=\mathbb{R}$ or $\mathbb{K}=\mathbb{C}$), together with a topology on $V$ such that vector addition and scalar multiplication are both continuous. Hilbert spaces and Banach spaces are examples of topological vector spaces.

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### The tensor product of two topological complexes with closed range

A Künneth formula by Grothendieck/Schwartz states the following: Let $A, B$ be chain complexes of nuclear Fréchet spaces. If the differentials $d_A, d_B$ are topological homomorphisms (meaning in ...
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### Strict topology and $*$-strong toppology on $B(H)$ coincide

In the paper Woronowicz - $C^*$-algebras generated by unbounded elements, I read that the $*$-strong operator topology on $B(H)$ and the strict topology on $B(H)$ coincide. I believe this means the ...
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### Is the unit ball of $A \odot B$ strictly dense in that of $M(A \otimes B)$?

Let $A$ and $B$ be $C^*$-algebras and let $A \otimes B$ their minimal tensor product and $M(A \otimes B)$ the associated multiplier algebra. On $M(A \otimes B)$, we consider the strict topology which ...
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### “Weakly” nuclear operators (terminology)

Recently, I'd come across the following kind of operators and I wonder if they have been considered before and given a name. Let's say that a linear map $T:V\to W$ between locally convex topological ...
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### Topological constraints on a compact convex set admitting a strictly convex and subdifferentiable real function

It is a theorem of Hervé that A compact convex set $K$ admits a strictly convex and continuous real function only if $K$ is metrizable. (The converse is also true.) I'm wondering if any results of ...
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### Can every contractible space be embedded as a convex subset of a vector space?

Given a contractible topological space $X$, is there (or what are some conditions for the existence of) a continuous embedding $\iota:X\hookrightarrow V$ into some topological vector space $V$ such ...
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### Reformulation - Construction of thermodynamic limit for GFF

I've posted a question about the thermodynamic limit for Gaussian Free Fields (GFF) a couple days ago and I haven't got any answers yet but I kept thinking about it and I thought it would be better to ...
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