Strictly Singular Uniform $\lambda-$Adjustment in Banach Spaces

TL;DR

This paper extends the concept of uniform λ-adjustment to sequences of subspaces and operators in Banach spaces, establishing stability results and posing new open questions about strict singularity and Banach space geometry.

Contribution

It introduces the notion of strictly singular uniform λ-adjustment for sequences of subspaces and operators, advancing the understanding of stability in Banach space theory.

Findings

Extended uniform λ-adjustment to sequences of subspaces and operators

Proved theorems on lower semi-Fredholm stability

Posed new open questions on strict singularity and Banach space geometry

Abstract

Based on the recently introduced uniform $\lambda-$adjustment for closed subspaces of Banach spaces we extend the concept of the strictly singular and finitely 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 spaces.