# Tagged Questions

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### how do I view the tensor product $X^*\otimes Y$ as a subspace of $\mathcal{L}(X,Y)$?

Background. According to Raymond A. Ryan, in his book Introduction to Tensor Products of Banach Spaces, a Banach ideal $\mathcal{J}$ is an assignment to each pair of Banach spaces $X$ and $Y$ a ...
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Let $X$ and $Y$ be Banach spaces. Denote by $X\otimes_\varepsilon Y$ the injective tensor product of $X$ and $Y$. Also, let $A\subset X, B\subset Y$ be any sets. Set $A\otimes B = \{a\otimes b\colon ... 1answer 65 views ### Image of the tensor product of strict maps of Banach spaces Let$f:A\to C$and$g:B\to D$be bounded linear maps of Banach spaces with closed image. Will$f\widehat{\otimes}g:A\widehat{\otimes}_\pi B\to C\widehat{\otimes}_\pi D$also have closed image? What ... 1answer 78 views ### Calculating the norm of$S\otimes T$for bounded linear$S,T$. Let$X,Y,W,Z$be Banach Spaces. Let$X\otimes_{\pi}Y$denote the tensor product endowed with the projective norm. If I have$S\in B(X,Z)$,$T\in B(Y,W)$, it is straightforward to show that$S\otimes ...
I want to show that $X\otimes(Y\otimes Z)$ is isomorphic to $(X\otimes Y)\otimes Z$. Intuitively I think I should just choose bases $\{e_{i}\}_{i\in I}, \{f_{j}\}_{j\in J}$, and $\{g_{k}\}_{k\in K}$ ...