On the continuity of the composition operation on spaces of holomorphic mappings
Abstract
We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fr\'echet space of the entire mappings that are bounded on bounded sets the composition turns to be even holomorphic. In such space we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.