On linear selections of convex set-valued mapsстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:We study continuous subadditive set-valued maps taking points of a linear space
$X$ to convex compact subsets of a linear space~$Y$. The subadditivity means that
$\varphi(x_1+x_2)\subset \varphi(x_1) + \varphi(x_2)$. We characterize all pairs
of locally convex spaces $(X, Y)$, for which any such map has a linear selection, i.e., a linear operator
$A\colon X \to Y$ such that $Ax \in \varphi (x)$, $x\in X$.
The existence of linear selections for a class of subadditive maps generated by
differences of a continuous function is proved. This result is applied to
the problem of Lipschitz stability of linear operators in Banach spaces.