Perturbation of linear operators on Banach spaces: some applications to Schauder bases and frames

摘要

In earlier papers we introduced and studied the notion of fractal operator that maps a continuous scalar valued function on a compact interval in RWe establish that the property of being bounded below and that of having a closed range are stable under the perturbation considered herein. As an immediate application, it is deduced that a given Schauder basis in X can be transformed to Schauder sequences. Perturbation of linear operators via an equation of the form ||Tx-x||=k||Tx-Lx||is also alluded and its application in constructing new Schauder bases from a given one is considered.