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Title: Complete Logarithmic Sobolev inequality via Ricci curvature bounded below II
We study the “geometric Ricci curvature lower bound”, introduced previously by Junge, Li and LaRacuente, for a variety of examples including group von Neumann algebras, free orthogonal quantum groups [Formula: see text], [Formula: see text]-deformed Gaussian algebras and quantum tori. In particular, we show that Laplace operator on [Formula: see text] admits a factorization through the Laplace–Beltrami operator on the classical orthogonal group, which establishes the first connection between these two operators. Based on a non-negative curvature condition, we obtain the completely bounded version of the modified log-Sobolev inequalities for the corresponding quantum Markov semigroups on the examples mentioned above. We also prove that the “geometric Ricci curvature lower bound” is stable under tensor products and amalgamated free products. As an application, we obtain a sharp Ricci curvature lower bound for word-length semigroups on free group factors.  more » « less
Award ID(s):
2000331
PAR ID:
10491990
Author(s) / Creator(s):
; ;
Publisher / Repository:
World Scientific
Date Published:
Journal Name:
Journal of Topology and Analysis
Volume:
15
Issue:
03
ISSN:
1793-5253
Page Range / eLocation ID:
741 to 794
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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