双线性形式，舒尔乘子，完全有界性和对偶性

Pub Date : 2023-10-26 DOI:10.7146/math.scand.a-140205

Erik Christensen

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引用次数: 1

摘要

关于算子和双线性形式的Grothendieck不等式暗示了复数$m \乘以n$矩阵的一些分解结果。基于算子空间和完全有界映射的理论，我们给出了这些结果的范数最优版本和两个与舒尔积相关的范数最优分解结果。我们证明了双线性形式的空间和舒尔乘子的空间在它们的完全有界范数方面是相互共轭对偶的。

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Bilinear forms, Schur multipliers, complete boundedness and duality

Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex $m \times n$ matrices. Based on the theory of operator spaces and completely bounded maps we present norm optimal versions of these results and two norm optimal factorization results related to the Schur product. We show that the spaces of bilinear forms and of Schur multipliers are conjugate duals to each other with respect to their completely bounded norms.

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