Stamate, Cristina About the lower semicontinuous regularization for vector functions. (English) Zbl 1076.47040 An. Științ. Univ. Al. I. Cuza Iași, Ser. Nouă, Mat. 50, No. 2, 407-414 (2004). 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 Keywords:lower level set; lower semicontinuous vector function; D.C. function; D.C. continuous functions PDFBibTeX XMLCite \textit{C. Stamate}, An. Științ. Univ. Al. I. Cuza Iași, Ser. Nouă, Mat. 50, No. 2, 407--414 (2004; Zbl 1076.47040)