The pressure in operator algebras

Abstract

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 Open image in new window at a self-adjoint element T in Open image in new window 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 invariant, and also prove that the pressure of the implementing inner automorphism of a crossed product Open image in new window ×α ℤ at a self-adjoint operator T in Open image in new window equals that of α at T.