双线性形式，舒尔乘子，完全有界性和对偶性

IF 0.3 4区数学 Q4 MATHEMATICS

Mathematica Scandinavica 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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.