Some points of view on Grothendieck's inequalities
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Some points of view on Grothendieck's inequalities. / Christensen, Erik.
I: Linear Algebra and Its Applications, Bind 691, 2024, s. 196-215.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Some points of view on Grothendieck's inequalities
AU - Christensen, Erik
N1 - Publisher Copyright: © 2024 The Author(s)
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