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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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.

Article information

Source
Commun. Math. Anal., Volume 19, Number 2 (2016), 62-67.

Dates
First available in Project Euclid: 14 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.cma/1473854217

Mathematical Reviews number (MathSciNet)
MR3512604

Zentralblatt MATH identifier
1361.46021

Subjects
Primary: 46B25: Classical Banach spaces in the general theory

Keywords
Banach Spaces sum of two closed subspaces closedness

Citation

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


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