集值余弦族的交换性

A. Smajdor, W. Smajdor
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引用次数: 1

摘要

设K为实Banach空间中一个内部非空的闭凸锥,令cc(K)表示K的所有非空凸紧子集的族。如果{Ft: t≥0}是连续可加集值函数Ft: K→cc(K)的正则余弦族,使得x∈Ft(x),当t≥0,且x∈K时,则$F_t \circ F_s (x) = F_s \circ F_t (x)fors,t \geqslant 0andx \in K$。
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Commutativity of set-valued cosine families
Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If {Ft: t ≥ 0} is a regular cosine family of continuous additive set-valued functions Ft: K → cc(K) such that x ∈ Ft(x) for t ≥ 0 and x ∈ K, then $F_t \circ F_s (x) = F_s \circ F_t (x)fors,t \geqslant 0andx \in K$.
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