Communications in Mathematical Analysis

A Note on Closedness of the Sum of Two Closed Subspaces in a Banach Space

Zhe-Ming Zheng and Hui-Sheng Ding

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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.

Article information

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

Banach Spaces sum of two closed subspaces closedness


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.

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