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The least slope of a convex function and the maximal monotonicity of its subdifferential

✍ Scribed by S. Simons

Publisher
Springer
Year
1991
Tongue
English
Weight
402 KB
Volume
71
Category
Article
ISSN
0022-3239

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In the paper we deal with the problem when the graph of the subdifferential operator of a convex lower semicontinuous function has a common point with the product of two convex nonempty weak and weak\* compact sets, i.e. when graph&j n (Q x Q\*) # 0. The results obtained partially solve the problem

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Let E be a separable Banach space with separable dual. We show that the operation of subdi erentiation and the inverse operation are Borel from the convex functions on E into the monotone operators on E (subspace of the closed sets of E Γ— E \* ) for the E ros-Borel structures. We also prove that th