RT Journal Article
T1 Disjointly strictly-singular inclusions between rearrangement invariant spaces
A1 García del Amo Jiménez, Alejandro José
A1 Hernández, Francisco L.
A1 Sánchez de los Reyes, Víctor Manuel
A1 Semenov, Evgeny M.
AB A linear operator between two Banach spaces X and Y is strictly-singular (or Kato) if it fails to be an isomorphism on any infinite dimensional subspace. A weaker notion for Banach lattices introduced in [8] is the following one: an operator T from a Banach lattice X to a Banach space Y is said to be disjointly strictly-singular if there is no disjoint sequence of non-null vectors (xn)n∈N in X such that the restriction of T to the subspace [(xn)∞n=1] spanned by the vectors (xn)n∈N is an isomorphism. Clearly every strictly-singular operator is disjointly strictly-singular but the converse is not true in general (consider for example the canonic inclusion Lq[0, 1]↪Lp[0, 1] for 1≤p<q<∞). In the special case of considering Banach lattices X with a Schauder basis of disjoint vectors both concepts coincide. The notion of disjointly strictly-singular has turned out to be a useful tool in the study of lattice structure of function spaces (cf. [7–9]). In general the class of all disjointly strictly-singular operators is not an operator ideal since it fails to be stable with respect to the composition on the right.The aim of this paper is to study when the inclusion operators between arbitrary rearrangement invariant function spaces E[0, 1] ≡ E on the probability space [0, 1] are disjointly strictly-singular operators.
PB London Mathematical Society
SN 1469-7750
YR 2000
FD 2000
LK https://hdl.handle.net/20.500.14352/58749
UL https://hdl.handle.net/20.500.14352/58749
DS Docta Complutense
RD 3 abr 2025