Resumen de Duality of tensor products of converge-free spaces

Gottfried Köthe

• Let $\lambda,\mu$ be two perfect convergence-free spaces. We prove the duallity theorem $$(\lambda\;\widetilde \otimes_n\mu)'_n \cong \lambda^x\; \widetilde\otimes_\epsilon\mu^x \mbox{ and } (\lambda\;\widetilde\otimes_\epsilon\mu)'_n\cong \lambda^x\;\widetilde\otimes_n\mu^x$$ where $n$ denotes the normal topology $T_n$ which coincides which Grothendieck's inductive topology on $\lambda\otimes\mu$.