2011/07/08 by Henri Bourlès, Bourlès, Henri
Mathematics · #18G50 #Analysis of PDEs (math.AP) #Category Theory (math.CT) #FOS: Mathematics #Optimization and Control (math.OC) #math.AP #math.CT #math.OC #msc:18G50
paper · pdf · doi:10.48550/arxiv.1107.1639
arxiv created 2013/02/22 · arxiv updated 2013/02/25
The spaces D, S and E' over ℝ^(n) are known to be flat modules over A=ℂ[∂1,...,∂n], whereas their duals D', S' and E are known to be injective modules over the same ring. Let A be a Noetherian k-algebra (k=ℝ or ℂ). The above observation leads us to study in this paper the link existing between the flatness of an A-module E which is a locally convex topological k-vector space and the injectivity of its dual. We show that, for dual pairs (E,E') which are (K) over A--a notion which is explained in the paper--, injectivity of E' is a stronger condition than flatness of E. A preprint of this paper (dated September 2009) has been quoted and discussed by Shankar.