Contractivity properties of Ornstein–Uhlenbeck semigroup for mixed q-Araki–Woods von Neumann algebras
- 1 November 2021
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 62 (11), 113502
- https://doi.org/10.1063/5.0057987
Abstract
We study certain non-tracial von Neumann algebras generated by some self-adjoint operators satisfying mixed q-commutation relations. Such algebras are discussed in the work of Bikram et al. [“Mixed q-deformed Araki-Woods von Neumann algebras,” (submitted)]. We prove the analog of Nelson’s hypercontractivity inequality for the mixed q-Ornstein–Uhlenbeck semigroup. We also show that the mixed q-Ornstein–Uhlenbeck semigroup is ultracontractive.Funding Information
- University Grants Commission (2121541041)
- ECR India (ECR/2018/001167)
This publication has 15 references indexed in Scilit:
- Approximation properties and absence of Cartan subalgebra for free Araki–Woods factorsAdvances in Mathematics, 2011
- Hypercontractivity on the q-Araki-Woods AlgebrasCommunications in Mathematical Physics, 2011
- Asymptotic matricial models and QWEP property for -Araki–Woods algebrasJournal of Functional Analysis, 2006
- Contractivity properties of Ornstein-Uhlenbeck semigroup for general commutation relationsMathematische Zeitschrift, 2005
- ULTRACONTRACTIVITY AND STRONG SOBOLEV INEQUALITY FOR q-ORNSTEIN–UHLENBECK SEMIGROUP (-1 < q < 1)Infinite Dimensional Analysis, Quantum Probability and Related Topics, 1999
- Free HypercontractivityCommunications in Mathematical Physics, 1997
- Completely positive maps on Coxeter groups, deformed commutation relations, and operator spacesMathematische Annalen, 1994
- Generalized statistics of macroscopic fieldsLetters in Mathematical Physics, 1993
- Applications of the complex interpolation method to a von Neumann algebra: Non-commutative Lp-spacesJournal of Functional Analysis, 1984
- The free Markoff fieldJournal of Functional Analysis, 1973