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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 .

Compact widths in metric trees

Asuman Güven Aksoy, Kyle Edward Kinneberg (2011)

Banach Center Publications

The definition of n-width of a bounded subset A in a normed linear space X is based on the existence of n-dimensional subspaces. Although the concept of an n-dimensional subspace is not available for metric trees, in this paper, using the properties of convex and compact subsets, we present a notion of n-widths for a metric tree, called Tn-widths. Later we discuss properties of Tn-widths, and show that the compact width is attained. A relationship between the compact widths and Tn-widths is also...

Compactness and convergence of set-valued measures

Kenny Koffi Siggini (2009)

Colloquium Mathematicae

We prove criteria for relative compactness in the space of set-valued measures whose values are compact convex sets in a Banach space, and we generalize to set-valued measures the famous theorem of Dieudonné on convergence of real non-negative regular measures.

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