2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129274Motivated by the interesting and yet scattered developments in representation theory of Banach-Lie groups, we discuss several functional analytic issues which should underlie the notion of infinite-dimensional reductive Lie group: norm ideals, triangular integrals, operator factorizations, and amenability.17 pagesRepresentation TheoryDifferential GeometryFunctional AnalysisPrimary 22E65; Secondary 22E46, 47B10, 47L20, 58B25text