Communications in Mathematical Analysis
- Commun. Math. Anal.
- Volume 19, Number 2 (2016), 62-67.
A Note on Closedness of the Sum of Two Closed Subspaces in a Banach Space
Let $X$ be a Banach space, and $M,N$ be two closed subspaces of $X$. We collect several necessary and sufficient conditions for the closedness of $M+N$ ($M+N$ is not necessarily direct sum), and show that a necessary condition in a classical textbook is also sufficient.
Commun. Math. Anal., Volume 19, Number 2 (2016), 62-67.
First available in Project Euclid: 14 September 2016
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46B25: Classical Banach spaces in the general theory
Zheng, Zhe-Ming; Ding, Hui-Sheng. A Note on Closedness of the Sum of Two Closed Subspaces in a Banach Space. Commun. Math. Anal. 19 (2016), no. 2, 62--67. https://projecteuclid.org/euclid.cma/1473854217