2019/07/15 by D'Onofrio, Luigi, Greco, Luigi, Perfekt, Karl-Mikael +2
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1907.06380
Given a Banach space E with a supremum-type norm induced by a collection of operators, we prove that E is a dual space and provide an atomic decomposition of its predual. We apply this result, and some results obtained previously by one of the authors, to the function space B introduced recently by Bourgain, Brezis, and Mironescu. This yields an atomic decomposition of the predual B_∗, the biduality result that B0^∗ = B_∗ and B_∗^∗ = B, and a formula for the distance from an element f ∈ B to B0.