摘要
设B与B′是两个实的Banach空间,f是B到B′的有界线性算子,X=(X_,F_,n≥1)是B值某种鞅型序列。本文证明了:X在有界线性算子变换下f(x)=(f(X_),F_,n≥1)的鞅型性质与某些积分性质不变。本文还给出了一些拟鞅变换局部收敛的结果,这些结果推广与改进了一些已知的结论。
Let B and B' be any two real Banach spaces, f is a bounded linear operator from B to B'. X=(X_n, F_n, n>1) is a martingale-like sequence of some type. In this paper we prove that f(X)=(f(X_n), F_n, n≥1) remains a mart ingale-like sequence of the same type as X ard inherit some properties of integrals of X. In the other direction some results of local convergence of quasi-martingle transforms are given. Some known results are extended and proved.
出处
《武汉大学学报（自然科学版）》
CSCD
1992年第1期1-10,共10页
Journal of Wuhan University(Natural Science Edition)
基金
国家自然科学基金
关键词
有界线性算子
拟鞅变换
局部收敛
invariance of bounded linear operator, quasi martingale trans form, local convergence, UMD space
