# Tagged Questions

Tensor products allow us to build "linear" objects from "multilinear" ones. It can refer to: basic ones from linear algebra/module theory, or more sophisticated versions from differential/algebraic geometry (bundles/sheaves), functional analysis (Hilbert/Banach/locally convex spaces), or in their ...

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### $\chi : \text{Hom}(M,A) \otimes \text{Hom}(A,N) \to \text{Hom}(M,N)$

Let $M,N$ be $A$-modules. Consider the map. $$\chi : \text{Hom}(M,A) \otimes \text{Hom}(A,N) \to \text{Hom}(M,N)$$ $$f \otimes g \mapsto g \circ f$$ If $M,N$ are projective I do know that $\chi$...
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### Can we embed $X'\otimes Y$ into the space of bounded, linear operators $X\to Y$?

Let $\mathbb F\in\left\{\mathbb C,\mathbb R\right\}$ $X$ and $Y$ be normed $\mathbb F$-vector spaces $X'$ denote the topological dual space of $X$ $\mathfrak L(X,Y)$ denote the space of bounded, ...
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### Are $X'\otimes Y$ and $\mathfrak L(X,Y)$ isomorphic?

Let $\mathbb F\in\left\{\mathbb C,\mathbb R\right\}$ $X$ and $Y$ be normed $\mathbb F$-vector spaces $X'$ be the topological dual space of $X$ $\mathfrak L(X,Y)$ be the set of bounded, linear ...
Let $$\otimes:R\times R\rightarrow W$$ $$f:R\times R\rightarrow R~~,~f(X,Y)=XY$$ $\otimes$ is tensor product, $W$ is a vector space, and $f$ is a bilinear may. As I know , we need to find a ...