关于复Hilbert空间中凸集的逼近映射  

PRXOIMITY MAPS FOR CONVEX SETS IN COMPLEX HILBERT SPACE

作　　者：钟新民[1] 

机构地区：[1]湖南师范大学数学系

出　　处：《湖南师范大学自然科学学报》1991年第4期297-301,共5页Journal of Natural Science of Hunan Normal University

摘　　要：设K是复Hilbert空间X中的闭凸集.任取x∈X,由定义映射P:x→y,P称为K的逼近映射,设P_i是K_i的逼近映射。本文证明了的充要条件是并证明了如K_1是紧集或K_1是有限维的,且存在X∈K_1,y∈K_2,使u∈K_1v∈K_2,则对任x∈K_1序列Q^nx收敛于Q的不动点,其中Q=P_1P_2.这样把u∈K_1v∈K_2W.Cheney关于实Hilbert空间的定理推广到复Hilbert空间.Let K be a closed convex set in complex Hilbert space X.For each x∈X,letp be the map defined by px∈K,‖px-x‖=‖z-x‖,p will be called the proxi-mity map for K.Let P_i denotes the proximity map for K_i,we prove that the suffi-cient and necessary condition for x=p_1p_2x is that‖u-v‖=‖x-p_2x‖.it's alsoproved that for each x∈K_1,the convergence of Q^nx to a fixed point of Q is assuredwhen either(a)K_1 is compact or(b)K_1 is finite dimensional and there existsx∈K_1 and y∈K_2 which satisfy‖u-v‖=‖x-y‖in which Q=P_1P_2.Thus theauthor generalizes Ward Cheney's theories in real Hilbert space to the case ofcomplex Hilbert space.

关 键 词：复希氏空间 凸集 逼近映射 紧集 

分 类 号：O177.92[理学—数学]