有界线性算子的不变性与拟鞅变换的局部收敛性

有界线性算子的不变性与拟鞅变换的局部收敛性 INVARIANCE OF BOUNDED LINEAR OPERATORS AND LOCAL CONVERGENCE OF QUASI-MARTINGALE TRANSFORMS 甘师信 Gan Shixin 1 first-author 武汉大学数学系 武汉大学数学系 Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 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. 有界线性算子的不变性 拟鞅变换 局部收敛性 UMD空间 invariance of bounded linear operator quasi martingale trans form local Convergence UMD space 国家自然科学基金(61672102) 1992-01-01 2021-04-01 1