This article is cited in 2 papers

Extension conditions for bounded linear and sublinear operators with values in Lindenstrauss spaces

Yu. È. Linke

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

Abstract: We find extension conditions for linear and sublinear operators with values in four classes of spaces: the spaces of continuous functions on a compact set, Lindenstrauss spaces, and their separable parts. We prove that in all these cases the extension property for linear operators implies the extension property for sublinear operators, while in separable spaces the two properties are equivalent.

Keywords: linear operator, sublinear operator, extension of operators, affine mapping, subdifferential, multivalued mapping, Lindenstrauss space.

UDC: 517.982+517.988

Received: 10.02.2010

 English version: Siberian Mathematical Journal, 2010, 51:6, 1061–1074

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