Asymptotic Estimates for Approximation Quantities of Tensor Product Identities Original Research Article

LetEnandFmbe two symmetric Banach spaces, andαa reasonable norm on their tensor product. We give asymptotically best possible estimates for the approximation and Gelfand numbers of the natural embedding from thenm-dimensional Hilbert spacelnm2intoEn⊗αFm, and its inverse. Our results are used in order to compute some related characteristics of such tensor products (e.g., type and cotype constants).