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Hypercontractivity of heat semigroups on free quantum groups
- Source :
- Journal of Operator Theory, Journal of Operator Theory, Theta Foundation, 2017, 77 (1), pp.61-76. ⟨10.7900/jot.2015nov13.2126⟩
- Publication Year :
- 2017
- Publisher :
- HAL CCSD, 2017.
-
Abstract
- In this paper we study two semigroups of completely positive unital self-adjoint maps on the von Neumann algebras of the free orthogonal quantum group $O_N^+$ and the free permutation quantum group $S_N^+$. We show that these semigroups satisfy ultracontractivity and hypercontractivity estimates. We also give results regarding spectral gap and logarithmic Sobolev inequalities.<br />19 pages
- Subjects :
- Pure mathematics
Logarithm
[MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA]
[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
01 natural sciences
Sobolev inequality
Permutation
symbols.namesake
Mathematics::Probability
0103 physical sciences
FOS: Mathematics
0101 mathematics
Operator Algebras (math.OA)
Quantum
ComputingMilieux_MISCELLANEOUS
Mathematics
Mathematics::Functional Analysis
Algebra and Number Theory
Mathematics::Operator Algebras
Quantum group
Unital
Probability (math.PR)
81R15, 81R50, 46L60
010102 general mathematics
Mathematics - Operator Algebras
Mathematics::Spectral Theory
Functional Analysis (math.FA)
Mathematics - Functional Analysis
symbols
Spectral gap
010307 mathematical physics
Mathematics - Probability
Von Neumann architecture
Subjects
Details
- Language :
- English
- ISSN :
- 03794024 and 18417744
- Database :
- OpenAIRE
- Journal :
- Journal of Operator Theory, Journal of Operator Theory, Theta Foundation, 2017, 77 (1), pp.61-76. ⟨10.7900/jot.2015nov13.2126⟩
- Accession number :
- edsair.doi.dedup.....f95deda1f33ee7cb23265bb26938f9f7
- Full Text :
- https://doi.org/10.7900/jot.2015nov13.2126⟩