【摘要】 研究了Lp( μ ,X)中的复一致凸和复局部一致凸性 ,得出了比Orlicz空间更强的结论 .即 :Lp( μ ,X)复一致凸的充要条件是X复一致凸 ;Lp( μ ,X)复局部一致凸的充要条件是对任意的x ∈S(Lp( μ ,X) )和ε >0 ,存在δ >0 ,对任意y ∈Lp( μ ,X) ,‖y｜A(x,y ,δ) ‖p =∫A(x,y ,δ)‖y(ω)‖pdy1p ≤ ε3　 ( 1 ≤p≤+∞ ) ,A(x ,y ,δ) =ω ∈Ω :14∑k‖x(ω) +ky(ω)‖ ≤ ( 1 +δ)‖x(ω)‖ .更多还原

【Abstract】 This thesis discuss complex uniform convexity and complex locally uniform convex ity of L p(μ,X) , and obtain better conclusions than those of Orlicz space . I.e.,a necessary and sufficient condition for complex uniform convexity of L p(μ,X) is complex uniform convexity of X ; a necessary and sufficient condition for complex locally uniform convexity of更多还原