THE CORRELATION NUMERICAL RANGE AND TRACE-POSITIVE COMPLEX POLYNOMIALS

Let A is an element of M-n(C). We prove that if W-c(A), the correlation numerical range introduced in [2], is a subset of [0,infinity), then A = P + D where P is positive semidefinite and D is a diagonal matrix such that Tr(D) = 0. This answers a question of D. Hadwin and D. Han. Additionally, we explore a few properties of W-c(A) and W-uc(A), another numerical range introduced in [2] that is closely related to Connes's Embedding Conjecture.