ABSTRACT

We completely characterize the left-symmetric points, the right-symmetric points, and the symmetric points in the sense of Birkhoff-James, in a Banach space. We obtain a complete characterization of the left-symmetric (right-symmetric) points in the infinity sum of two Banach spaces, in terms of the left-symmetric (right-symmetric) points of the constituent spaces. As an application of this characterization, we explicitly identify the left-symmetric (right-symmetric) points of some well-known three-dimensional polyhedral Banach spaces.

中文翻译：

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Banach空间中对称点的研究

摘要

我们在 Banach 空间中完全表征了 Birkhoff-James 意义上的左对称点、右对称点和对称点。根据组成空间的左对称（右对称）点，我们获得了两个 Banach 空间的无穷和中左对称（右对称）点的完整表征。作为这种表征的应用，我们明确地识别了一些著名的三维多面体 Banach 空间的左对称（右对称）点。