Disjointly strictly singular inclusions of symmetric spaces

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.

Embeddings of rearrangement invariant spaces that are not strictly singular

We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L1([0, 1]) is strictly singular if and only if G does not embed into E continuously, where G is the closure of the simple functions in the Orlicz space LΦ with Φ(x) = exp(x 2) − 1. In this paper we ask the following question. Given a rearrangement invariant space E on [0, 1], whe...

Embeddings of Rearrangement Invariant Spaces That Are Not Strictly Singular

We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L1 ((0; 1]) is strictly singular if and only if G does not embed into E continuously, where G is the closure of the simple functions in the Orlicz space L with (x) = exp(x 2) ? 1. In this paper we ask the following question. Given a rearrangement invariant space E on 0; 1], when ...

Strictly Singular Uniform λ−Adjustment in Banach Spaces

Based on the recently introduced uniform λ−adjustment for closed subspaces of Banach spaces we extend the concept of the strictly singular and nitely strictly singular operators to the sequences of closed subspaces and operators in Banach spaces and prove theorems about lower semi Fredholm stability. We also state some new open questions related to strict singularity and the geometry of Banach ...

Compact and strictly singular operators on certain function spaces