Strict quasicomplements and the operators of dense imbedding - Shevchik, V. V. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
A quasicomplement М ofasubspace N of a Banach space X is called strict if M does not contain an infinite-dimensional subspace M_1, such that the linear manifold N + M_1, is closed. It is proved that if X is separable, then N always has a strict quasicomplement. We study the properties of the dense imbedding operator restricted to infinite-dimensional closed subspaces of the space, where it is defined.