A FAMILY OF NON-COCYCLE CONJUGATE E-0-SEMIGROUPS OBTAINED FROM BOUNDARY WEIGHT DOUBLES

作者：Jankowski Christopher^*

来源：Journal of Operator Theory, 2013, 69(1): 233-256.

DOI：10.7900/jot.2010oct06.1889

• E-0-semigroup
• completely positive map
• q-positive map

Let rho is an element of M-n (C)* and rho%26apos; is an element of M-n%26apos; (C)* be states, and define unital q-positive maps phi and psi by phi (A) = rho (A) I-n and psi (D) = rho%26apos; (D)I-n%26apos; for all A is an element of M-n(C) and D is an element of M-n%26apos; (C). We show that if v and eta are type II Powers weights, then the boundary weight doubles (0,v) and (psi,eta) induce non-cocycle conjugate E-0-sernigroups if p and rho%26apos; have different eigenvalue lists. We then classify the q-corners and hyper maximal q-corners from phi to psi, finding that if v is a type II Powers weight of the form v( root I - Lambda(1) B root I - Lambda(1)) = (f,B f), where Lambda(1) is an element of B(L-2(0, infinity)) is the operator of multiplication by e(-x), then the E-0-semigroups induced by (phi, v) and (psi,v) are cocycle conjugate if and only if n = n%26apos; and phi and psi are conjugate.

• 出版日期2013