We study Banach spaces whose group of isometries acts micro-transitively on the unit sphere. We introduce a weaker property, which one-complemented subspaces inherit, that we call uniform micro-semitransitivity. We prove a number of results about both micro-transitive and uniformly micro-semitransitive spaces, including that they are uniformly convex and uniformly smooth, and that they form a self-dual class. To this end, we relate the fact that the group of isometries acts micro-transitively with a property of operators called the pointwise Bishop-Phelps-Bollob\'as property and use some known results on it. Besides, we show that if there is a non-Hilbertian non-separable Banach space with uniform micro-semitransitive (or micro-transitive) norm, then there is a non-Hilbertian separable one. Finally, we show that an $L_p(\mu)$ space is micro-transitive or uniformly micro-semitransitive only when $p=2$.

中文翻译：

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在 Banach 空间上，其等距组微传递作用于单位球面

我们研究 Banach 空间，其等距组在单位球面上微传递。我们引入了一个较弱的性质，一个互补的子空间继承了它，我们称之为均匀微半传递性。我们证明了一些关于微传递空间和一致微半传递空间的结果，包括它们是一致凸的和一致光滑的，并且它们形成了一个自对偶类。为此，我们将等距组微传递地与称为逐点 Bishop-Phelps-Bollob 的算子属性相关联，并在其上使用一些已知结果。此外，我们证明，如果存在具有均匀微半传递（或微传递）范数的非希尔伯特不可分巴拿赫空间，则存在非希尔伯特可分空间。最后，