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- W2097681077 abstract "We have seen that if phi: M_n(C) rightarrow M_n(C) is a unital q-positive map and nu is a type II Powers weight, then the boundary weight double (phi, nu) induces a unique (up to conjugacy) type II_0 E_0-semigroup. Let phi: M_n(C) rightarrow M_n(C) and psi: M_{n'}(C) rightarrow M_{n'}(C) be unital rank one q-positive maps, so for some states rho in M_n(C)^* and rho' in M_{n'}(C)^*, we have phi(A)=rho(A)I_n and psi(D) = rho'(D)I_{n'} for all A in M_n(C) and D in M_{n'}(C). We find that if nu and eta are arbitrary type II Powers weights, then (phi, nu) and (psi, eta) induce non-cocycle conjugate E_0-semigroups if rho and rho' have different eigenvalue lists. We then completely classify the q-corners and hyper maximal q-corners from phi to psi, obtaining the following result: If nu is a type II Powers weight of the form nu(sqrt{I - Lambda(1)} B sqrt{I - Lambda(1)})=(f,Bf), then the E_0-semigroups induced by (phi,nu) and (psi, nu) are cocycle conjugate if and only if n=n' and phi and psi are conjugate." @default.
- W2097681077 created "2016-06-24" @default.
- W2097681077 creator A5057179364 @default.
- W2097681077 date "2010-07-26" @default.
- W2097681077 modified "2023-09-27" @default.
- W2097681077 title "A family of non-cocycle conjugate E_0-semigroups obtained from boundary weight doubles" @default.
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