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Application of Michael's theorem and its converse to sublinear operators

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Abstract

A theorem of Michael on continuous selectors and its converse are used in this article to study subdifferentials of continuous sublinear operators with values in a cone of lower semicontinuous functions. It is proved that such operators are subdifferentiable (i.e., have nonempty subdifferentials) if their domains are separable Banach spaces. Sublinear operators that are not subdifferentiable are found.

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Authors and Affiliations

  1. Irkutsk Computer Center, USSR

    Yu. É. Linke

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  1. Yu. É. Linke
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Translated from Matematicheskie Zametki, Vol. 52, No. 1, pp. 67–75, July, 1992.

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Linke, Y.É. Application of Michael's theorem and its converse to sublinear operators. Math Notes 52, 680–686 (1992). https://doi.org/10.1007/BF01247650

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  • DOI: https://doi.org/10.1007/BF01247650

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