Yilmaz Y.2024-08-042024-08-0420091230-3429https://doi.org/10.12775/TMNA.2009.023https://hdl.handle.net/11616/91052Our main interest in this work is to characterize certain operator spaces acting on some important vector-valued function spaces such as (V a)a?A c0 , by introducing a new kind basis notion for general Topological vector spaces. Where A is an infinite set, each Va is a Banach space and (Va) a?A c0 is the linear space of all functions x:A ? ?Va such that, for each ? > 0, the set {a ? A : ?xa? > ?} is finite or empty. This is especially important for the vector-valued sequence spaces (V i)i?N c0 because of its fundamental place in the theory of the operator spaces (see, for example, [12]). © 2009 Juliusz Schauder Center for Nonlinear Studies.eninfo:eu-repo/semantics/openAccessBiorthogonal systemsGeneralization of basesOperators on function spacesRepresentation of operatorsSchauder basesVector-valued function spacesArticle33233535310.12775/TMNA.2009.0232-s2.0-77956477136Q2