A sufficient condition for the sum of complemented subspaces to be complemented

• Published in: Доповіді НАН України
• Date: 2019
• Main Author: Feshchenko, I.S.
• Format: Article
• Language: English
• Published: Видавничий дім "Академперіодика" НАН України 2019
• Subjects: Математика
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/150462
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A sufficient condition for the sum of complemented subspaces to be complemented / I.S. Feshchenko // Доповіді Національної академії наук України. — 2019. — № 1. — С. 10-15. — Бібліогр.: 13 назв. — англ.

We provide a sufficient condition for the sum of a finite number of complemented subspaces of a Banach space to be complemented. Under this condition, the formula for a projection onto the sum is given. The condition is sharp (in a certain sense). As an application, we provide a sufficient conditi...