Cartan–Slodkowski spectra, splitting elements and noncommutative spectral mapping theorems

In this paper, we prove Slodkowski version of the infinite-dimensional spectral mapping theorem and Cartan–Slodkowski version of the finite-dimensional spectral mapping theorem for nilpotent operator Lie subalgebras with respect to the various noncommutative functional calculi. © 2005 Elsevier Inc. All rights reserved.