巴拿赫空间 J 和中的投影

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-09-17 DOI:10.1007/s13398-024-01654-4

Manuel González, Javier Pello

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引用次数: 0

摘要

我们研究了贝勒诺引入的巴拿赫空间的 J-sums \(J(\Phi)\)和 \({\hat{J}}(\Phi)\)中的一些投影族。作为一个应用，我们证明了在某些条件下， \(J(\Phi )\) 和 \({\hat{J}}(\Phi )\) 是子投影的，也就是说，它们中的每一个封闭的无穷维子空间都包含一个被补的无穷维子空间。

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Projections in the J-sums of Banach spaces

We study some families of projections in the J-sums of Banach spaces \(J(\Phi )\) and \({\hat{J}}(\Phi )\) introduced by Bellenot. As an application, we show that, under some conditions, \(J(\Phi )\) and \({\hat{J}}(\Phi )\) are subprojective, i.e., every closed infinite-dimensional subspace of either of them contains a complemented infinite-dimensional subspace.

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

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