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Singlevaluedness of monotone operators on subspaces of GSG spaces

Martin Heisler — 1996

Commentationes Mathematicae Universitatis Carolinae

We extend Zajíček’s theorem from [Za] about points of singlevaluedness of monotone operators on Asplund spaces. Namely we prove that every monotone operator on a subspace of a Banach space containing densely a continuous image of an Asplund space (these spaces are called GSG spaces) is singlevalued on the whole space except a $σ$ -cone supported set.

Remarks on continuous images of Radon-Nikodým compacta

Marián J. Fabián; Martin Heisler; Eva Matoušková — 1998

Commentationes Mathematicae Universitatis Carolinae

A family of compact spaces containing continuous images of Radon-Nikod’ym compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikod’ym compact $K$ we prove: If $K$ is totally disconnected, then it is Radon-Nikod’ym compact. If $K$ is adequate, then it is even Eberlein compact.

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