Remarks on strictly singular operators

Abstract

A continuous linear operator T : E → F is called strictly singular if it cannot be invertible on any infinite dimensional closed subspace of its domain. In this note we discuss sufficient conditions and consequences of the phenomenon LB(E, F ) = L s (E, F ), which means that every continuous linear bounded operator defined on E into F is strictly singular.2010 Mathematics Subject Classification. 46A03, 46A11, 46A32, 46A45.