2021/02/01 by Karsten Kruse, Kruse, Karsten
Mathematics · #Advanced Banach Space Theory #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematik #Schauder basis #Schauder decomposition #injective tensor product #series representation #vector-valued function
paper · doi:10.15480/882.3173
openalex publication_date 2021/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/01
It is a classical result that every (Formula presented.) -valued holomorphic function has a local power series representation. This even remains true for holomorphic functions with values in a locally complete locally convex Hausdorff space E over (Formula presented.). Motivated by this example we try to answer the following question. Let E be a locally convex Hausdorff space over a field (Formula presented.), let (Formula presented.) be a locally convex Hausdorff space of (Formula presented.) -valued functions on a set Ω and let (Formula presented.) be an E-valued counterpart of (Formula presented.) (where the term E-valued counterpart needs clarification itself). For which spaces is it possible to lift series representations of elements of (Formula presented.) to elements of (Formula presented.) ? We derive sufficient conditions for the answer to be affirmative using Schauder decompositions which are applicable for many classical spaces of functions (Formula presented.) having an equicontinuous Schauder basis.