%0 Journal Article %T Non-commutative Functional Calculus and Spectral Theory %A Jim Agler %A John E. McCarthy %J Mathematics %D 2015 %I arXiv %X We develop a functional calculus for $d$-tuples of non-commuting elements in a Banach algebra. The functions we apply are free analytic functions, that is nc functions that are bounded on certain polynomial polyhedra. %U http://arxiv.org/abs/1504.07323v1