Strictly singular and strictly co-singular inclusions between symmetric sequence spaces

Compact and strictly singular operators on certain function spaces

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...

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 ...

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.

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 ...