Abstract.
The existence of infinite dimensional closed linear spaces of holomorphic functions f on a domain G in the complex plane such that Tf has dense images on certain subsets of G, where T is a continuous linear operator, is analyzed. Necessary and sufficient conditions for T to have the latter property are provided and applied to obtain a number of concrete examples: infinite order differential operators, composition operators and multiplication operators, among others.
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This work was supported in part by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 and by MEC DGES Grants MTM2006-13997-C02-01 and MTM2004-21420-E.
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Bernal-González, L., Calderón-Moreno, M.C. & Prado-Bassas, J.A. Holomorphic Operators Generating Dense Images. Integr. equ. oper. theory 60, 1–11 (2008). https://doi.org/10.1007/s00020-007-1547-4
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DOI: https://doi.org/10.1007/s00020-007-1547-4