The Pressure in Operator Algebras  

作　　者：Cheng Jun HOU 

机构地区：[1]Department of Mathematics, Qufu Normal University, Qufu 273165, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第6期983-996,共14页数学学报（英文版）

基　　金：the NNSF of China (Grant No.A0324614);NSF of Shandong (Grant No.Y2006A03);NSF of QFNU (Grant No.xj0502)

摘　　要：We introduce two notions of the pressure in operator algebras, one is the pressure Pα（π, T） for an automorphism α of a unital exact C^＊-algebra A at a self-adjoint element T in A with respect to a faithful unital ＊-representation π the other is the pressure Pτ,α（T） for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ. We give some properties of the pressure, show that it is a conjugate invaxiant, and also prove that the pressure of the implementing inner automorphism of a crossed product A×α Z at a self-adjoint operator T in A equals that of α at T.We introduce two notions of the pressure in operator algebras, one is the pressure Pα（π, T） for an automorphism α of a unital exact C^＊-algebra A at a self-adjoint element T in A with respect to a faithful unital ＊-representation π the other is the pressure Pτ,α（T） for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ. We give some properties of the pressure, show that it is a conjugate invaxiant, and also prove that the pressure of the implementing inner automorphism of a crossed product A×α Z at a self-adjoint operator T in A equals that of α at T.

关 键 词：exact C^＊-algebra hyperfinite von Neumann algebra ENTROPY PRESSURE crossed product 

分 类 号：O177.5[理学—数学]