Some points of view on Grothendieck's inequalities
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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.
Original language | English |
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Journal | Linear Algebra and Its Applications |
Volume | 691 |
Pages (from-to) | 196-215 |
Number of pages | 20 |
ISSN | 0024-3795 |
DOIs | |
Publication status | Published - 2024 |
Bibliographical note
Publisher Copyright:
© 2024 The Author(s)
- Bilinear operators, Completely bounded, Duality, Grothendieck inequality, Operator space, Schur product, Stinespring representation, Tensor product
Research areas
ID: 389670738