论文标题
巴拉奇空间及其球的正常瓷砖
Normal tilings of a Banach space and its ball
论文作者
论文摘要
我们展示了有关巴拉克空间中瓷砖的一些新结果。 Banach Space $ X $的平铺是用非空内部装置的封闭套装的封面，因此它们具有成对的脱节内部。如果此外，瓷砖的内部半径均匀地从下方界定，外部半径均匀地从上方界限，我们说瓷砖是正常的。 2010年，Preiss构建了可分离的希尔伯特空间的凸正常瓷砖。对于带有Schauder的Banach空间，我们将证明Preiss的结果仍然是星形瓷砖而不是凸面的结果。另外，每当$ x $均匀凸出时，我们就会提供单位球体，单位球或任何凸形主体的凸的正常斜利的精确结构。
We show some new results about tilings in Banach spaces. A tiling of a Banach space $X$ is a covering by closed sets with non-empty interior so that they have pairwise disjoint interiors. If moreover the tiles have inner radii uniformly bounded from below, and outer radii uniformly bounded from above, we say that the tiling is normal. In 2010 Preiss constructed a convex normal tiling of the separable Hilbert space. For Banach spaces with Schauder basis we will show that Preiss' result is still true with starshaped tiles instead of convex ones. Also, whenever $X$ is uniformly convex we give precise constructions of convex normal tilings of the unit sphere, the unit ball or in general of any convex body.
