Onl p-complemented copies in Orlicz spaces

Disjointly strictly singular inclusions of symmetric spaces

“…In parallel, we shall show that condition (A) is necessary and sufficient for the identity inclusion operator from one Lorentz space into another to have the DSS property (and similar assertion for Marcinkiewicz spaces). These results also supplement the theorem for Orlicz spaces proved in [5] and cited above.…”

“…By (A), ||x k || M (φ) → ∞ as k → ∞, which contradicts condition (5). This completes the proof of Theorem 2.…”

Some remarks on thin operators

“…Proposition 3. 10. Let E(· ) and F (· 0 ) be order-continuous K othe function spaces such that E 0 is order continuous, E satis¯es the R-condition, F is disjointly subprojective and [s(E); ¼ (E)]\[s(F ); ¼ (F )] = ?.…”

“…Y a bounded operator. We say that T is disjointly strictly singular (see [10]) if there is no disjoint sequence of non-null vectors (x n ) n in E such that the restriction of T to the subspace [x n ] spanned by the sequence (x n ) n is an isomorphism. Clearly, every strictly singular operator de ned on a Banach lattice is disjointly strictly singular, but the converse is not true (f.i.…”

Singularities of embedding operators between symmetric function spaces on [0, 1]

“…In particular, in [11], the following two lemmas were formulated. Now, following [13], we introduce the weak version of strict singularity mentioned in the beginning of this section. Let X be a quasi-Banach lattice and Y a Banach or quasi-Banach space.…”