Hypercontractivity for a quantum Ornstein-Uhlenbeck semigroup

• 成果类型: Article
• 署名作者: Carbone, Raffaella; Sasso, Emanuela
• 署名单位: University of Pavia; University of Genoa
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0073-2
• 发表日期: 2008
• 页码: 505-522
• 关键词: logarithmic sobolev inequalities

摘要

We prove hypercontractivity for a quantum Ornstein-Uhlenbeck semigroup on the entire algebra B(h) of bounded operators on a separable Hilbert space h. We exploit the particular structure of the spectrum together with hypercontractivity of the corresponding birth and death process and a proper decomposition of the domain. Then we deduce a logarithmic Sobolev inequality for the semigroup and gain an elementary estimate of the best constant.