Some points of view on Grothendieck's inequalities

Centre for Symmetry and Deformation

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Some points of view on Grothendieck's inequalities. / Christensen, Erik.

In: Linear Algebra and Its Applications, Vol. 691, 2024, p. 196-215.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Christensen, E 2024, 'Some points of view on Grothendieck's inequalities', Linear Algebra and Its Applications, vol. 691, pp. 196-215. https://doi.org/10.1016/j.laa.2024.03.016

APA

Christensen, E. (2024). Some points of view on Grothendieck's inequalities. Linear Algebra and Its Applications, 691, 196-215. https://doi.org/10.1016/j.laa.2024.03.016

Vancouver

Christensen E. Some points of view on Grothendieck's inequalities. Linear Algebra and Its Applications. 2024;691:196-215. https://doi.org/10.1016/j.laa.2024.03.016

Author

Christensen, Erik. / Some points of view on Grothendieck's inequalities. In: Linear Algebra and Its Applications. 2024 ; Vol. 691. pp. 196-215.

Bibtex

@article{6357295ab7cb477da19dd72f9c083e90,

title = "Some points of view on Grothendieck's inequalities",

abstract = "Haagerup's proof of the non commutative little Grothendieck inequality raises some questions on the commutative little inequality, and it offers a new result on scalar matrices with non negative entries. The theory of completely bounded maps may be used to show that the commutative Grothendieck inequality follows from the little commutative inequality, and that this passage may be given a geometric form as a relation between a pair of compact convex sets of positive matrices, which, in turn, characterizes the little constant kGC.",

keywords = "Bilinear operators, Completely bounded, Duality, Grothendieck inequality, Operator space, Schur product, Stinespring representation, Tensor product",

author = "Erik Christensen",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

year = "2024",

doi = "10.1016/j.laa.2024.03.016",

language = "English",

volume = "691",

pages = "196--215",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Some points of view on Grothendieck's inequalities

AU - Christensen, Erik

PY - 2024

Y1 - 2024

N2 - Haagerup's proof of the non commutative little Grothendieck inequality raises some questions on the commutative little inequality, and it offers a new result on scalar matrices with non negative entries. The theory of completely bounded maps may be used to show that the commutative Grothendieck inequality follows from the little commutative inequality, and that this passage may be given a geometric form as a relation between a pair of compact convex sets of positive matrices, which, in turn, characterizes the little constant kGC.

AB - Haagerup's proof of the non commutative little Grothendieck inequality raises some questions on the commutative little inequality, and it offers a new result on scalar matrices with non negative entries. The theory of completely bounded maps may be used to show that the commutative Grothendieck inequality follows from the little commutative inequality, and that this passage may be given a geometric form as a relation between a pair of compact convex sets of positive matrices, which, in turn, characterizes the little constant kGC.

KW - Bilinear operators

KW - Completely bounded

KW - Duality

KW - Grothendieck inequality

KW - Operator space

KW - Schur product

KW - Stinespring representation

KW - Tensor product

U2 - 10.1016/j.laa.2024.03.016

DO - 10.1016/j.laa.2024.03.016

M3 - Journal article

AN - SCOPUS:85189473743

VL - 691

SP - 196

EP - 215

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

ID: 389670738