摘要
本文证明了一个Banach空间B同构于Hilbert空间当且仅当不等式 C_1Eφ(S^((2))(f))≤Eφ(f~*)≤C_2Eφ(S^((2))(f))成立。其中f=(f_n)是取值于B中的鞅,φ:[0,∞)→[0,∞)是单调增加的连续凸函数,且满足φ(0)=0及增长条件φ(2λ)≤Cφ(λ) λ≥0C_1与C_2是仅与空间B及函数φ有关的正常数。
In this paper, we prove: A Banach space B is isomorphic to a Hilbert space iff the inequality C_1Eφ(S^((2))(f))≤Eφ(f~*)≤C_2Eφ(S^((2))(f)) holds for every martingale f=(f_n) with values in B, where φ is a continuous increasing convex function from [0, ∞) into [0, ∞) satisfying φ(0)=0 and growth condition α(2λ)≤Cφ(λ) (?)λ≥0 and the choice of C_1 and C_2 depends only on the space B and the function φ.
出处
《武汉大学学报（自然科学版）》
CSCD
1991年第3期29-34,共6页
Journal of Wuhan University(Natural Science Edition)
