Singlevaluedness of monotone operators on subspaces of GSG spaces

Martin Heisler

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 2, page 255-261
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Heisler, Martin. "Singlevaluedness of monotone operators on subspaces of GSG spaces." Commentationes Mathematicae Universitatis Carolinae 37.2 (1996): 255-261. <http://eudml.org/doc/247892>.

@article{Heisler1996,
abstract = {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 $\sigma $-cone supported set.},
author = {Heisler, Martin},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Asplund spaces; GSG spaces; monotone operators; countable dentability; points of singlevaluedness; monotone operators on Asplund spaces; GSG spaces; -cone supported set},
language = {eng},
number = {2},
pages = {255-261},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Singlevaluedness of monotone operators on subspaces of GSG spaces},
url = {http://eudml.org/doc/247892},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Heisler, Martin
TI - Singlevaluedness of monotone operators on subspaces of GSG spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 2
SP - 255
EP - 261
AB - 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 $\sigma $-cone supported set.
LA - eng
KW - Asplund spaces; GSG spaces; monotone operators; countable dentability; points of singlevaluedness; monotone operators on Asplund spaces; GSG spaces; -cone supported set
UR - http://eudml.org/doc/247892
ER -

References

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  1. Christensen J.P.R., Kenderov P.S., Dense strong continuity of mappings and the RadonNikodým property, Math. Scand. (1984), 54 70-78. (1984) MR0753064
  2. Diestel J., Geometry of Banach Spaces - Selected Topics, Lecture Notes in Mathematics, vol. 485 Springer Verlag (1975). (1975) Zbl0307.46009MR0461094
  3. Fabian M., Weak Asplund Spaces, Lecture Notes (in preparation) (1995). (1995) 
  4. Phelps R.R., Convex Functions, Monotone Operators and Differentiability, Lecture Notes in Math. 1364 Springer Verlag (1989). (1989) Zbl0658.46035MR0984602
  5. Stegall Ch., The Radon-Nikodým property in conjugate Banach spaces II., Trans. Amer. Math. Soc. (1981), 264 507-519. (1981) Zbl0475.46016MR0603779
  6. Zajíček L., Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces, Czech. Math. Journal 41 (116) (1991), 288-296. (1991) MR1105445

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