In this paper we continue the study of Lorentz sequence spaces d(w,p), 0 < p < 1, initiated by N. Popa [8]. First we show that the Mackey completion of d(w,p) is equal to d(v, 1) for some sequence v. Next, we prove that if d(w, p) (2 h, then it contains a complemented subspace isomorphic to lp. Finally we show that if limn_1(X)"=1 wi)1 = °°, tnen every complemented subspace of d(w,p) with symme...

Let 1 < p ̸= 2 < ∞, ε > 0 and let T : lp(l2) into → Lp[0, 1] be an isomorphism Then there is a subspace Y ⊂ lp(l2), (1 + ε)-isomorphic to lp(l2), such that: T|Y is an (1+ ε)-isomorphism and T (Y ) is Kp-complemented in Lp [0, 1], with Kp depending only on p. Moreover, Kp ≤ (1 + ε)γp if p > 2 and Kp ≤ (1 + ε)γp/(p−1) if 1 < p < 2, where γr is the Lr norm of a standard Gaussian variable.

We study some structural aspects of the subspaces of the non-commutative (Haagerup) Lp-spaces associated with a general (non necessarily semi-finite) von Neumann algebra a. If a subspace X of Lp(a) contains uniformly the spaces lnp , n ≥ 1, it contains an almost isometric, almost 1-complemented copy of lp. If X contains uniformly the finite dimensional Schatten classes S p , it contains their l...

Abstract. It is shown that for an L1-predual space X and a countable linearly independent subset of ext(BX∗) whose norm-closed linear span Y in X∗ is w∗-closed, there exists a w∗-continuous contractive projection from X∗ onto Y . This result combined with those of Pelczynski and Bourgain yields a simple proof of the Lazar-Lindenstrauss theorem that every separable L1-predual with non-separable ...

This paper deals with certain properties of the subspaces of LC(H) and C and namely those connected with the reflexivity and with the property of containing classical spaces. It is proved that any subspace of C (1 < p < oo) is either isomorphic to Hilbert space or it contains a subspace isomorphic to I . For Cj and LC'H) the same results were obtained by J. R. Holub, cf. [4]. Introduction. Let ...

We prove that if X is a subspace of Lp (2 < p < ∞), then either X embeds isomorphically into `p ⊕ `2 or X contains a subspace Y, which is isomorphic to `p(`2). We also give an intrinsic characterization of when X embeds into `p⊕`2 in terms of weakly null trees in X or, equivalently, in terms of the “infinite asymptotic game” played in X. This solves problems concerning small subspaces of Lp ori...