关于Frchet空间诱导极限的Dieudonn-Schwartz定理(英文)

DIEUDONNE-SCHWARTZ THEOREM IN INDUCTIVE LIMITS OF FRECHET SPACES

设(E,ξ)=indlim(E_n,ξ_n)为(LF)—空间,则(DST)成立若下述两个条件之一被满足: (Ⅰ)存在自然数序列n_1<n_2<n_3<…使对于每个自然数i成立,这里记E_(n_i)在(E_(n_(i+2)),ξ_(n_(i+2)))中的闭包; (Ⅱ)对于每个自然数n,存在(E_n,ξ_n)中o的圆凸邻城U_n及自然数m(n)使且span[U_n^E]闭于(E_m,ξ_m),对于任意m>m(n)。

Let (E,)=indlim(En) be an (LF)-space. Then (DST) holds if one of the following two conditions is satisfied:(I) there exists a sequence of natural numbers n1<n2<n3<*** such that EniEnl+z EW1+1 for every i N, where EmiEmi+2 denotes the closure of Emi in(Eml+2,) for any n^N, there exists an absolutely convex, neighborhoodUn of o in () and m(n) N such that UmE Em(mM and span(UmE) is closed in (Em) for any m>m(n).1991 Mathematics Subject Classification. Primary 46A03; 46A13.