2014/11/17 by Schechtman, Gideon
#46B20 #46B28 #47B10 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1411.4427
The paper contains three results, the common feature of which is that they deal with the Schatten p class. The first is a presentation of a new complemented subspace of Cp in the reflexive range (and p\not= 2). This construction answers a question of Arazy and Lindestrauss from 1975. The second result relates to tight embeddings of finite dimensional subspaces of Cp in Cpn with small n and shows that ℓpk nicely embeds into Cpn only if n is at least proportional to k (and then of course the dimension of Cpn is at least of order k2). The third result concerns single element of Cpn and shows that for p>2 any n× n matrix of Cp norm one and zero diagonal admits, for every ε>0, a k-paving of Cp norm at most ε with k depending on ε and p only.