Injectivity of spaces of bounded vector sequences and spaces of operators
Various Banach or Fréchet spaces which are either vector-valued sequence spaces or components of some closed operator ideals are considered. Complete solutions are given to the problem of their injectivity or embeddability as complemented subspaces in dual Fréchet spaces. The problem of complementability of components of a given closed operator ideal in the corresponding components of another closed operator ideal is considered as well and some new results are obtained. All these results are obtained by application of a “universal” method introduced in this paper.