Unbounded strictly singular operators

Domination by Positive Disjointly Strictly Singular Operators

We prove that each positive operator from a Banach lattice E to a Banach lattice F with a disjointly strictly singular majorant is itself disjointly strictly singular provided the norm on F is order continuous. We prove as well that if S : E → E is dominated by a disjointly strictly singular operator, then S2 is disjointly strictly singular.

operators on L ( L p ) and ` p - strictly singular operators

A classification of weakly compact multiplication operators on L(Lp), 1 < p < ∞, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of `p-strictly singular operators, and we also investigate the structure of general `p-strictly singular operators on Lp . The main result is that if an operator T on Lp , 1 < p < 2, is `p-strictly singula...

Compact and strictly singular operators on certain function spaces

Strictly Singular Non-compact Operators on Hereditarily Indecomposable Banach Spaces

An example is given of a strictly singular non-compact operator on a Hereditarily Indecomposable, reflexive, asymptotic `1 Banach space. The construction of this operator relies on the existence of transfinite c0-spreading models in the dual of the space.

NARROW AND l2-STRICTLY SINGULAR OPERATORS FROM Lp

In the first part of the paper we prove that for 2 < p, r < ∞ every operator T : Lp → lr is narrow. This completes the list of sequence and function Lebesgue spaces X with the property that every operator T : Lp → X is narrow. Next, using similar methods we prove that every l2-strictly singular operator from Lp, 1 < p < ∞, to any Banach space with an unconditional basis, is narrow, which partia...