STRICTLY SINGULAR OPERATORS IN ASYMPTOTIC e_p BANACH SPACES

摘要

We present a condition on higher order asymptotic behavior of basic sequences in a Banach space ensuring the existence of bounded noncompact strictly singular operators on a subspace. Applications concern asymptotic e_p spaces, 1 ≤ p ＜ ∞, in particular convexified mixed Tsirelson spaces and related asymptotic e_p HI spaces.