On the Injective Tensor Product of Distinguished Frechet Spaces

✍ Scribed by Juan Carlos Díaz; Pawel Domaeski

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 525 KB
• Volume: 198
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19991980104

✦ Synopsis

An example of two distinguished M c h e t spaces E, F is given (even more, E is quasinormable and F is normable) such that their completed injective tensor product E&F is not distinguished. On the other hand, it is proved that for arbitrary reflexive F r k h e t space E and arbitrary compact set K the space of E -valued continuous functions C ( K , E) is distinguished and it,s strong dual is naturally isomorphic to Li (p)&EL where L i ( p ) = C ( K ) ' .