On quotients of ideals of weighted holomorphic mappings

Abstract

We explore the procedure given by left-hand quotients in the context of weighted holomorphic ideals. On the one hand, we show that this procedure does not generate new ideals other than the ideal of weighted holomorphic mappings when considering the left-hand quotients induced by the ideals of $p$-compact, weakly $p$-compact, unconditionally $p$-compact, approximable or right $p$-nuclear operators with their respective weighted holomorphic ideals. On the other hand, the procedure is of interest when considering other operators ideals as it provides new weighted holomorphic ideals. This is the case of the ideal of Grothendieck weighted holomorphic mappings or the ideal of Rosenthal weighted holomorphic mappings, where the applicability of this construction is shown.