摘要
Let(S, Σ, μ) be a complete positive σ-finite measure space and let X be a Banach space. We consider the simultaneous proximinality problem in Lp(S, Σ, X) for 1 p < +∞. We establish some N-simultaneous proximinality results of Lp(S, Σ0, Y) in Lp(S, Σ, X) without the Radon-Nikody′m property(RNP) assumptions on the space span Y and its dual span Y*, where Σ0is a sub-σ-algebra of Σ and Y a nonempty locally weakly compact closed convex subset of X. In particular, we completely solve one open problem and partially solve another one in Luo et al.(2011).
Let（S, Σ, μ） be a complete positive σ-finite measure space and let X be a Banach space. We consider the simultaneous proximinality problem in Lp（S, Σ, X） for 1 p 〈 ＋∞. We establish some N-simultaneous proximinality results of Lp（S, Σ0, Y） in Lp（S, Σ, X） without the Radon-Nikody′m property（RNP） assumptions on the space span Y and its dual span Y＊, where Σ0is a sub-σ-algebra of Σ and Y a nonempty locally weakly compact closed convex subset of X. In particular, we completely solve one open problem and partially solve another one in Luo et al.（2011）.
基金
supported by National Natural Science Foundation of China(Grant Nos.11101363,11171300 and 11371325)
Natural Science Foundation of Zhejiang Province(Grant No.LY12A01029)
