Universal spaces for the subdifferentials of sublinear operators with values in the spaces of continuous functions |
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Authors: | Yu È Linke |
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Institution: | 1.Institute for System Dynamics and Control Theory,Irkutsk,Russia |
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Abstract: | Given a continuous sublinear operator P: V → C(X) from a Hausdorff separable locally convex space V to the Banach space C(X) of continuous functions on a compact set X we prove that the subdifferential ∂P at zero is operator-affinely homeomorphic to the compact subdifferential ∂
c
Q, i.e., the subdifferential consisting only of compact linear operators, of some compact sublinear operator Q: ł2 → C(X) from a separable Hilbert space ł2, where the spaces of operators are endowed with the pointwise convergence topology. From the topological viewpoint, this
means that the space L
c
(ł2, C(X)) of compact linear operators with the pointwise convergence topology is universal with respect to the embedding of the subdifferentials
of sublinear operators of the class under consideration. |
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Keywords: | |
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