A note on closedness of the sum of two closed subspaces in a Banach space

Abstract

Let $X$ be a Banach space, and $M,N$ be two closed subspaces of $X$. We present several necessary and sufficient conditions for the closedness of $M+N$ ($M+N$ is not necessarily direct sum).

Cited by in corpus (1)

• Completeness of Sums of Subspace of Bounded Functions and Applications