Strict quasicomplements and the operators of dense imbedding

  • V. V. Shevchik

Abstract

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.
Published
25.06.1994
How to Cite
ShevchikV. V. “Strict Quasicomplements and the Operators of Dense Imbedding”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 46, no. 6, June 1994, pp. 789–792, https://umj.imath.kiev.ua/index.php/umj/article/view/5710.
Section
Short communications