We study the presence of copies of ln p ’s uniformly in the spaces 2(C[0, 1],X) and 1(C[0, 1],X). By using Dvoretzky’s theorem we deduce that if X is an infinite- dimensional Banach space, then 2(C[0, 1],X) contains p2-uniformly copies of ln∞’s and 1(C[0, 1],X) contains -uniformly copies of ln 2 ’s for all > 1. As an application, we show that if X is an infinite-dimensional Banach space then the spaces 2(C[0, 1],X) and 1(C[0, 1],X) are distinct, extending the well-known result that the spaces 2(C[0, 1],X) and N(C[0, 1],X) are distinct., Dumitru Popa., and Seznam literatury
The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the solutions of classical problems in option pricing theory in Mathematical Finance.