An operator-valued free Poincarè inequality

• Autorzy: Ito, Hyuga
• Języki publikacji: EN

Abstrakty

EN

The purpose of this short note is to give an operator-valued free Poincarè inequality, which provides a simple proof to (an improvement of) a lemma of Voiculescu (2000) asserting that the kernel of the free difference quotient is exactly the coefficients.

Słowa kluczowe

EN

Sobolev space; free difference quotient; projective tensor product; conditional expectation; von Neumann algebra

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2023
• Tom: Vol. 43, Fasc. 2
• Strony: 241--246
• Opis fizyczny: Bibliogr. 7 poz..

Twórcy

autor

Ito, Hyuga

• Graduate School of Mathematics, Nagoya University, Nagoya, 464-0862, Japan,

Bibliografia

• [1] U. Haagerup, The Grothendieck inequality for bilinear forms on C∗-algebras, Adv. Math. 56 (1985), 93-116.
• [2] H. Ito, Differential calculus for fully matricial functions I, preprint (2023).
• [3] H. Ito, Free analysis on non-commutative Grassmannian manifolds, in preparation.
• [4] J. Mingo and R. Speicher, Free Probability and Random Matrices, Fields Inst. Monogr. 35, Springer, 2017.
• [5] D. Voiculescu, The analogues of entropy and of Fisher’s information measure in free probability theory V. Noncommutative Hilbert transforms, Invent. Math. 132 (1998), 189-227.
• [6] D. Voiculescu, The coalgebra of the free difference quotient and free probability, Int. Math. Res. Notices 2000, 79-106.
• [7] Problems posed during the workshop “Free Analysis” at American Institute of Mathematics, 2006; https://aimath.org/WWN/freeanalysis/freeanalysis.pdf.