2021/09/30 by Ciaci, Stefano, Langemets, Johann, Lissitsin, Aleksei
#46B04 (Primary) #46B20 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2109.15001
We extend the (attaining of) strong diameter two property to infinite cardinals. In particular, a Banach space has the 1-norming attaining strong diameter two property with respect to ω (1-ASD2Pω for short) if every convex series of slices of the unit ball intersects the unit sphere. We characterize C(K) spaces and L1(μ) spaces having the 1-ASD2Pω. We establish dual implications between the 1-ASD2Pω, ω-octahedral norms and Banach spaces failing the (-1)-ball-covering property. The stability of these new properties under direct sums and tensor products is also investigated.