On a norming property of subspaces of a Banach space and some applications

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.