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 ...

In this article we investigate disjointly non-singular (DNS) operators. Following [9] say that an operator T from a Banach lattice F into space E is DNS, if no restriction of to subspace generated by disjoint sequence strictly singular. We partially answer question showing class operators forms open subset L(F,E) as soon order continuous. Moreover, show in case DNS and only the norm topology mi...