有限von Neumann代数上一类迹函数的若干性质
Some Properties of a Class of Trace Functions on Finite von Neumann Algebras
摘要: 本文在有限von Neumann代数的情形下应用广义奇异值的方法证明了一类迹函数的若干性质。特别地,我们将Hansen的主要结果推广至有限von Neumann代数的情形。
Abstract: In this paper, via the method of generalized singular values, we prove some properties of a class of trace functions defined over finite von Neumann algebras. In particular, we extend the main results of Hansen to the context of finite von Neumann algebras.
参考文献
|
[1]
|
Shi, G. and Hansen, F. (2020) Variational Representations Related to Tsallis Relative Entropy. Letters in Mathematical Physics, 110, 2203-2220. [Google Scholar] [CrossRef]
|
|
[2]
|
Lieb, E.H. and Ruskai, M.B. (1973) Proof of the Strong Subadditivity of Quantum-Mechanical Entropy. Journal of Mathematical Physics, 14, 1938-1941. [Google Scholar] [CrossRef]
|
|
[3]
|
Lieb, E.H. (1973) Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture. Advances in Mathematics, 11, 267-288. [Google Scholar] [CrossRef]
|
|
[4]
|
Hansen, F., Liang, J. and Shi, G. (2017) Peierls-Bogolyubov’s Inequality for Deformed Exponentials. Entropy, 19, Article 271. [Google Scholar] [CrossRef]
|
|
[5]
|
Pisier, G. and Xu, Q. (2003) Noncommutative-Spaces. In: Handbook of the Geometry of Banach Spaces, North-Holland, 1459-1517.
|
|
[6]
|
Fack, T. and Kosaki, H. (1986) Generalized S-Numbers of-Measure Operators. Pacific Journal of Mathematics, 123, 269-300.
|
|
[7]
|
Ma, N., Zhao X. and Zhang, Y. (2024) On Some Properties for a Class of Deformed Trace Functions on Finite Von Neumann Algebras, Manuscript.
|
|
[8]
|
Petz, D. (1985) Spectral Scale of Self-Adjoint Operators and Trace Inequalities. Journal of Mathematical Analysis and Applications, 109, 74-82. [Google Scholar] [CrossRef]
|
|
[9]
|
Hansen, F. and Pedersen, G.K. (1995) Perturbation Formulas for Traces on C-Algebras. Publications of the Research Institute for Mathematical Sciences, 31, 169-178. [Google Scholar] [CrossRef]
|