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Commutativity of set-valued cosine families

Andrzej Smajdor, Wilhelmina Smajdor (2014)

Open Mathematics

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 F t: t ≥ 0 is a regular cosine family of continuous additive set-valued functions F t: K → cc(K) such that x ∈ F t(x) for t ≥ 0 and x ∈ K, then F t F s ( x ) = F s F t ( x ) f o r s , t 0 a n d x K .

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