On Property (M) and Its Generalizations

  title={On Property (M) and Its Generalizations},
  author={Hong-Kun Xu and Giuseppe Marino and Paolamaria Pietramala},
  journal={Journal of Mathematical Analysis and Applications},
Abstract Properties strict (M) and uniform (M) are introduced. It is shown that if X has property (M) and is uniformly convex in every direction, then X has both strict (M) and uniform (M). It is also shown that if X* is separable, then strict (M) implies uniform (M) and property (M) implies weak uniform normal structure. Relations with other geometrical properties of Banach spaces are also discussed. 

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