Strict quasicomplements and the operators of dense imbedding

• Date: 1994
• Main Authors: Shevchik, V. V., Шевчик, В. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1994
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5710
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 propert...