2019/12/11 by Angrisani, Francesca, Ascione, Giacomo, D'Onofrio, Luigi +1
#26A16 #47B44 #47G10 #54E45 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1912.05187
For a compact metric space (K, ρ), the predual of Lip(K, ρ) can be identified with the normed space M(K) of finite (signed) Borel measures on K equipped with the Kantorovich-Rubinstein norm, this is due to Kantorovich [20]. Here we deduce atomic decomposition of M(K) by mean of some results from [10]. It is also known, under suitable assumption, that there is a natural isometric isomorphism between Lip(K, ρ) and (lip(K, ρ))** [15]. In this work we also show that the pair (lip(K, ρ), Lip(K, ρ)) can be framed in the theory of o-O type structures introduced by K. M. Perfekt.