Finitely strictly singular operators in harmonic analysis and function theory

Compact and strictly singular operators on certain function spaces

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...

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.

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...

Descriptive Set Theoretic Methods Applied to Strictly Singular and Strictly Cosingular Operators

The class of strictly singular operators originating from the dual of a separable Banach space is written as an increasing union of ω1 subclasses which are defined using the Schreier sets. A question of J. Diestel, of whether a similar result can be stated for strictly cosingular operators, is studied.