Restricted Invertibility and the Banach-Mazur distance to the cube
Restricted Invertibility and the Banach-Mazur distance to the cube
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受限可逆性和到立方体的 Banach-Mazur 距离
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发表时间：
2012
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通讯作者：
Pierre Youssef
中科院分区：
文献类型：
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作者：
Pierre Youssef
我们证明了Spielman-Srivastava获得的限制性可逆性原则的归一化版本。应用此结果，我们获得了比例Dvoretzky-Rogers分解定理的新证据，以恢复最佳当前估计值。结果，我们还恢复了Banach-Mazur距离与立方体的最著名估计：每个N维规范空间与ELL _ {infty}^n的距离最多是（2n）^（5/6）。最后，使用Batson-Spielman-Srivastava的工作中的工具，我们为Kashin-Tzafriri定理提供了有关受限矩阵规范的新证明。
We prove a normalized version of the restricted invertibility principle obtained by Spielman-Srivastava. Applying this result, we get a new proof of the proportional Dvoretzky-Rogers factorization theorem recovering the best current estimate. As a consequence, we also recover the best known estimate for the Banach-Mazur distance to the cube: the distance of every n-dimensional normed space from ell_{infty}^n is at most (2n)^(5/6). Finally, using tools from the work of Batson-Spielman-Srivastava, we give a new proof for a theorem of Kashin-Tzafriri on the norm of restricted matrices.