2018/04/20 by Karim Khanaki, Khanaki, Karim
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO) #math.FA #math.LO
paper · pdf · doi:10.48550/arxiv.1804.08446
The primary classification for this submission is Functional Analysis. This paper is companion-piece to arXiv:1603.08134 Comments are welcome ([email protected])
arxiv created 2018/04/20 · arxiv updated 2018/04/24
A separable Banach space X is said to be finitely determined if for each separable space Y such that X is finitely representable (f.r.) in Y and Y is f.r. in X then Y is isometric to X. We provide a direct proof (without model theory) of the fact that every finitely determined space X (isometrically) contains every (separable) space Y which is finitely representable in X. We also point out how a similar argument proves the Krivine-Maurey theorem on stable Banach spaces, and give the model theoretic interpretations of some results.