On the Injective Tensor Product of Distinguished Frechet Spaces

摘要

AbstractAn example of two distinguished Fréchet spacesE, Fis given (even more,Eis quasinormable andFis normable) such that their completed injective tensor productE⊗Fis not distinguished. On the other hand, it is proved that for arbitrary reflexive Fréchet spaceEand arbitrary compact setKthe space ofE‐ valued continuous functionsC(K, E)is distinguished and its strong dual is naturally isomorphic to ⊗ whereL1(μ