2019-06-182019-06-182002-06Bernal González, L., Calderón Moreno, M.d.C. y Grosse-Erdmann, K. (2002). Strongly omnipresent operators: general conditions and applications to composition operators. Journal of the Australian Mathematical Society, 72 (3), 335-348.1446-78871446-8107https://hdl.handle.net/11441/87495This paper studies the concept of strongly omnipresent operators that was recently introduced by the first two authors. An operator T on the space H(G) of holomorphic functions on a complex domain G is called strongly omnipresent whenever the set of T-monsters is residual in H(G), and a T-monster is a function f such that T f exhibits an extremely ‘wild’ behaviour near the boundary. We obtain sufficient conditions under which an operator is strongly omnipresent, in particular, we show that every onto linear operator is strongly omnipresent. Using these criteria we completely characterize strongly omnipresent composition and multiplication operators.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Holomorphic functionT-monsterResidual setStrongly omnipresent operatorDense rangeLocally dense rangeLocally stable operatorComposition operatorLeftcomposition operatorMultiplication operatorinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1017/S1446788700036764