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Let $X$ be a locally convex space, and $\{Y_i;\ i\in I\}$ a covariant system of locally convex spaces over a partially ordered set $I$, i.e. a system of linear continuous mappings is given $\sigma^j_i …

Let me start with the following Illustration: Let $G$ be a compact group, and let $\pi:G\to H$ be its (surjective) continuous homomorphism onto a (compact) group $H$. So we can think that $H$ is the …

Let $G$ be a locally compact Abelian group (we can think that $G={\mathbb R}$). Let $C_0(G)$ be the space of continuous functions $u:G\to{\mathbb C}$ vanishing at infinity with the usual $\sup$-norm, …

This continues my question of two months ago. Let $X$ be a compact Hausdorff topological space. We consider the $C^*$-algebra $C(X)$ of continuous functions on $X$, its dual space $C(X)^{*}=M(X)$ of m …

I have no intuition in this field so excuse me if this is trivial. Let $X$ be a compact Hausdorff space, and $C(X)$ the algebra of continuous functions on $X$ with the usual $\sup$-norm. This is a $C^ …

Let $X$ be a compact Hausdorff topological space and $C(X)$ the Banach algebra of continuous functions $u:X\to\mathbb C$ (with the usual $\sup$-norm). It is well-known that the structure of Banach alg …

I would say that this is not well-known: It is well-known that a Banach space $V$ is always Pontryagin-reflexive, i.e. the natural map $V\to \text{Hom}_\mathbb{R}(\text{Hom}_\mathbb{R}(V, \mathbb{R}) …

I am reading K.D.Bierstedt's paper Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. I. Journal für die reine und angewandte Mathematik 259 (1973): 186-210. It is wr …

Let $X$ be a locally convex space, $T$ a balanced convex compact set in $X$, and $f:X\to\mathbb{C}$ a linear functional which is (not necessarily continuous on $X$, but) continuous on $T$. It is not d …

There are four most important functional spaces in analysis: the space $\mathcal{C}(M)$ of continuous functions on a topological space, the space $\mathcal{E}(M)$ of smooth functions on a smooth man …

Suppose $M$ is a complex affine algebraic manifold in ${\mathbb C}^n$ (I mean, a set of common zeroes of a system of polynomials on ${\mathbb C}^n$, which is at the same time a smooth manifold). Consi …

In the theory of stereotype spaces there is a series of natural functors that satisfy this identity with one of the two main tensor products (the so-called ``injective stereotype tensor product'' $\od …

Let $X$ and $Y$ be locally convex spaces, and $\varphi: X\to Y$ a linear continuous mapping. Suppose first that $S$ is a compact set in $X$. Then $\varphi$, being considered as a mapping from $S$ to $ …

I asked this a week ago at math.stackexchange, but without success. As far as I understand, there are several meanings of the notion of the Köthe sequence space, in particular, Hans Jarchow in his "L …

A.Defant and K.Floret in chapter 7 of their Tensor Norms and Operator Ideals prove the equality $$ L_1(\mu\times\nu)\cong L_1(\mu)\widehat{\otimes}L_1(\nu) $$ for measures $\mu$ and $\nu$. At the same …