Article

Full entry | PDF   (0.1 MB)
Keywords:
Asplund spaces; GSG spaces; monotone operators; countable dentability
Summary:
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.
References:
Christensen J.P.R., Kenderov P.S.: Dense strong continuity of mappings and the RadonNikodým property. Math. Scand. (1984), 54 70-78. MR 0753064
Diestel J.: Geometry of Banach Spaces - Selected Topics. Lecture Notes in Mathematics, vol. 485 Springer Verlag (1975). MR 0461094 | Zbl 0307.46009
Fabian M.: Weak Asplund Spaces. Lecture Notes (in preparation) (1995).
Phelps R.R.: Convex Functions, Monotone Operators and Differentiability. Lecture Notes in Math. 1364 Springer Verlag (1989). MR 0984602 | Zbl 0658.46035
Stegall Ch.: The Radon-Nikodým property in conjugate Banach spaces II. Trans. Amer. Math. Soc. (1981), 264 507-519. MR 0603779 | Zbl 0475.46016
Zajíček L.: Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces. Czech. Math. Journal 41 (116) (1991), 288-296. MR 1105445

Partner of