On spectra of Lüders operations
Gabriel Nagy · Journal of Mathematical Physics · 2008
We show that all the eigenvalues of certain generalized Lüders operations are non-negative real numbers in two cases of interest. In particular, given a commuting n-tuple A=(A1,…,An) consisting of positive operators on a Hilbert space H, satisfying ∑j=1nAj=I, we show that the spectrum of the Lüders operation: ΛA:B(H)∋X↦∑j=1nAj1∕2XAj1∕2∈B(H) is contained in [0,∞), so the only solution of the equation ΛA(X)=I−X is the “expected” one: X=12I.