2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62980We prove that if T is a strictly singular 1-1 operator defined on an infinite dimensional Banach space X, then for every infinite dimensional subspace Y of X there exists an infinite dimensional subspace Z of Y such that Z contains orbits of T of every finite length and the restriction of T on Z is a compact operator.See also: http://www.math.sc.edu/~giorgis/research.htmlFunctional Analysis47B07,46B03text