三线性算子空间Grothendieck定理的失效

IF 1 3区数学 Q1 MATHEMATICS Discrete Analysis Pub Date : 2018-12-23 DOI:10.19086/da.8805

J. Briet, C. Palazuelos

{"title":"三线性算子空间Grothendieck定理的失效","authors":"J. Briet, C. Palazuelos","doi":"10.19086/da.8805","DOIUrl":null,"url":null,"abstract":"We give a counterexample to a trilinear version of the operator space Grothendieck theorem. In particular, we show that for trilinear forms on l∞, the ratio of the symmetrized completely bounded norm and the jointly completely bounded norm is in general unbounded. The proof is based on a non-commutative version of the generalized von Neumann inequality from additive combinatorics.","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2018-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Failure of the trilinear operator space Grothendieck theorem\",\"authors\":\"J. Briet, C. Palazuelos\",\"doi\":\"10.19086/da.8805\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a counterexample to a trilinear version of the operator space Grothendieck theorem. In particular, we show that for trilinear forms on l∞, the ratio of the symmetrized completely bounded norm and the jointly completely bounded norm is in general unbounded. The proof is based on a non-commutative version of the generalized von Neumann inequality from additive combinatorics.\",\"PeriodicalId\":37312,\"journal\":{\"name\":\"Discrete Analysis\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2018-12-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.19086/da.8805\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.19086/da.8805","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

我们给出了算子空间格罗滕迪克定理的一个三线性版本的反例。特别地，我们证明了对于l∞上的三线性形式，对称完全有界范数与联合完全有界范数之比一般是无界的。该证明是基于可加组合学中广义冯·诺伊曼不等式的非交换版本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Failure of the trilinear operator space Grothendieck theorem

We give a counterexample to a trilinear version of the operator space Grothendieck theorem. In particular, we show that for trilinear forms on l∞, the ratio of the symmetrized completely bounded norm and the jointly completely bounded norm is in general unbounded. The proof is based on a non-commutative version of the generalized von Neumann inequality from additive combinatorics.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete Analysis Mathematics-Algebra and Number Theory

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

17 weeks

期刊介绍： Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.

期刊最新文献

Stronger arithmetic equivalence Random volumes in d-dimensional polytopes Joints formed by lines and a $k$-plane, and a discrete estimate of Kakeya type An efficient container lemma A characterization of polynomials whose high powers have non-negative coefficients