Non-commutative Lebesgue decomposition of non-commutative measures
Non-commutative Lebesgue decomposition of non-commutative measures
A positive non-commutative (NC) measure is a positive linear functional on the free disk operator system which is generated by a $d$-tuple of non-commuting isometries. By introducing the hybrid forms, their Cauchy transforms, and techniques from NC reproducing kernel Hilbert spaces (RKHS), we construct a natural Lebesgue decomposition for any …