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Sibirsk. Mat. Zh., 2011, Volume 52, Number 3, Pages 635–649 (Mi smj2225)  

Universal spaces for the subdifferentials of sublinear operators with values in the spaces of continuous functions

Yu. È. Linke

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk

Abstract: Given a continuous sublinear operator $P\colon V\to C(X)$ 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 $\partial P$ at zero is operator-affinely homeomorphic to the compact subdifferential $\partial^cQ$, i.e., the subdifferential consisting only of compact linear operators, of some compact sublinear operator $Q\colon\ell^2\to C(X)$ from a separable Hilbert space $\ell^2$, where the spaces of operators are endowed with the pointwise convergence topology. From the topological viewpoint, this means that the space $L^c(\ell^2,C(X))$ 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.

Keywords: sublinear operator, subdifferential, compact subdifferential, compact sublinear operator, multivalued mapping, continuous selector, homeomorphism, affine homeomorphism, operator-affine homeomorphism, embedding.

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English version:
Siberian Mathematical Journal, 2011, 52:3, 501–511

Bibliographic databases:

UDC: 517.982+517.988
Received: 16.12.2008

Citation: Yu. È. Linke, “Universal spaces for the subdifferentials of sublinear operators with values in the spaces of continuous functions”, Sibirsk. Mat. Zh., 52:3 (2011), 635–649; Siberian Math. J., 52:3 (2011), 501–511

Citation in format AMSBIB
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\paper Universal spaces for the subdifferentials of sublinear operators with values in the spaces of continuous functions
\jour Sibirsk. Mat. Zh.
\yr 2011
\vol 52
\issue 3
\pages 635--649
\mathnet{http://mi.mathnet.ru/smj2225}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858648}
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\jour Siberian Math. J.
\yr 2011
\vol 52
\issue 3
\pages 501--511
\crossref{https://doi.org/10.1134/S0037446611030128}
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