dimanche 7 décembre 2014

tensor products


Let $E_{1},\cdots, E_{n}$ be Banach spaces; $n\in\mathbb{N}$ and $\mathbb{R}$ be a real numbers and $E\widehat{\otimes}\mathbb{R}$ be a completion tensor product. We have the fact that $E_{i}\widehat{\otimes}\mathbb{R}\equiv E_{i}$ for all $i=1,\cdots,n$.


Does $E_{1}\widehat{\otimes}\mathbb{R}\times\cdots\times E_{1}\widehat{\otimes}\mathbb{R}\equiv E_{1}\times\cdots\times E_{n}$?





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