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2016 A Note on Closedness of the Sum of Two Closed Subspaces in a Banach Space
Zhe-Ming Zheng, Hui-Sheng Ding
Commun. Math. Anal. 19(2): 62-67 (2016).

Abstract

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.

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Zhe-Ming Zheng. Hui-Sheng Ding. "A Note on Closedness of the Sum of Two Closed Subspaces in a Banach Space." Commun. Math. Anal. 19 (2) 62 - 67, 2016.

Information

Published: 2016
First available in Project Euclid: 14 September 2016

zbMATH: 1361.46021
MathSciNet: MR3512604

Subjects:
Primary: 46B25

Keywords: ‎Banach spaces , closedness , sum of two closed subspaces

Rights: Copyright © 2016 Mathematical Research Publishers

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Vol.19 • No. 2 • 2016
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