In this talk we first introduce a notion of dominated splitting for M(2,C) sequences and show an energy parameter belongs to the spectrum of a Jacobi operator, possibly singular, if and only if the associated Jacobi cocycle does not admit dominated splitting. Then we consider dynamically defined Jacobi operators whose base dynamics is only assumed to be topologically transitive. We show an energy parameter belongs to the spectrum of the operator defined by a base point with a dense orbit if and only if the dynamically defined Jacobi cocycle does not admit dominated splitting. This extends both the original Johnson's theorem for Schrodinger operators and a previous result obtained by Chris Marx for certain dynamically defined Jacobi operators. This is a joint work with Kateryna Alkorn.