We introduce and study m-heavy subspaces of a Banach space and obtain a complete analytic characterization of the same. The importance of m-heavy subspaces in studying the geometry of a Banach space is illustrated by establishing its various applications, including a strengthening of the classical Birkhoff–James orthogonality, duality theory and linear Hahn–Banach extension operators.

中文翻译：

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Banach空间子空间的规范性及其应用

我们介绍和研究Banach 空间的m-重子空间，并获得其完整的解析表征。m重子空间在研究 Banach 空间几何中的重要性通过建立其各种应用来说明，包括加强经典 Birkhoff-James 正交性、对偶理论和线性 Hahn-Banach 扩展算子。