Geometrical properties of Banach spaces generated by sublinear operators

摘要

We solve a problem posed by Mastylo (Math Japon 36(1), 85–92, 1991) proving that every “non-trivial” subspace of a Banach space X generated by some positive sublinear operator and an L p -space with 1 ≤  p < ∞ contains, for any ({varepsilon > 0}) , an ({(1 + varepsilon)}) -copy of l p which is ({(1 + varepsilon)}) -complemented in X.