2019
Том 71
№ 11

# Strict quasicomplements and the operators of dense imbedding

Shevchik V. V.

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.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 6, pp 863-867.

Citation Example: Shevchik V. V. Strict quasicomplements and the operators of dense imbedding // Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 789–792.

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