On the necessity of the Moreau-Rockafellar-Robinson qualification condition in Banach spaces
On the necessity of the Moreau-Rockafellar-Robinson qualification condition in Banach spaces
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论Banach空间中Moreau-Rockafellar-Robinson资格条件的必要性
DOI：
10.1007/s10107-007-0162-0
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发表时间：
2008
影响因子：
2.7
通讯作者：
M. Théra
中科院分区：
文献类型：
--
作者：
E. Ernst;M. Théra
众所周知，Moreau-Rockafellar-罗宾逊内点限定条件足以保证定义在局部凸空间上的两个扩展实值凸下半连续函数的共轭的下底卷积是精确的，并且这些函数的和的次微分是它们的次微分的和.本文致力于证明这个条件在某种意义上也是必要的，只要底层空间是Banach空间。我们的结果是基于Banach空间的拓扑对偶的任何弱 *-闭和凸无界线性有界子集的非支撑弱 *-闭超平面的存在性。
As well known, the Moreau-Rockafellar-Robinson internal point qualification condition is sufficient to ensure that the infimal convolution of the conjugates of two extended-real-valued convex lower semi-continuous functions defined on a locally convex space is exact, and that the subdifferential of the sum of these functions is the sum of their subdifferentials. This note is devoted to proving that this condition is, in a certain sense, also necessary, provided the underlying space is a Banach space. Our result is based upon the existence of a non-supporting weak*-closed hyperplane to any weak*-closed and convex unbounded linearly bounded subset of the topological dual of a Banach space.