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About the lower semicontinuous regularization for vector functions. (English) Zbl 1076.47040

Summary: This paper extends the lower semicontinuous regularization for vector functions from the case of Hilbert-space-valued maps to the case of maps taking values in Banach complete lattices and locally convex complete order lattices. The main result is applied to obtain a locally convex, continuous decomposition for local D.C. (= expressible as a difference of convex maps) continuous functions taking values in a Banach lattice.

MSC:

47H04 Set-valued operators
47L07 Convex sets and cones of operators
46B42 Banach lattices
28B05 Vector-valued set functions, measures and integrals
46A40 Ordered topological linear spaces, vector lattices
49J45 Methods involving semicontinuity and convergence; relaxation
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