Continuous extension operators and convexity |
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| Authors: | Eva Kopecká Simeon Reich |
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| Institution: | aInstitute of Mathematics, Czech Academy of Sciences, ?itná 25, CZ-11567 Prague, Czech Republic;bDepartment of Mathematics, The Technion–Israel Institute of Technology, 32000 Haifa, Israel |
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| Abstract: | Given a nonempty closed subset A of a Hilbert space X, we denote by L(A) the space of all bounded Lipschitz mappings from A into X, equipped with the supremum norm. We show that there is a continuous mapping Fc:L(A)?L(X) such that for each g∈L(A), Fc(g)|A=g,  , and  . We also prove that the corresponding set-valued extension operator is lower semicontinuous. |
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| Keywords: | MSC: 46C05 47H04 47H09 54C20 54C60 54C65 |
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