  We provide characterizations of Anosov representations of word hyperbolic
groups into real semisimple Lie groups in terms of the existence of equivariant
limit maps on the Gromov boundary, the Cartan property and the uniform gap
summation property introduced by Guichard-Gu\'eritaud-Kassel-Wienhard. We also
study representations of finitely generated groups satisfying weak uniform gaps
in eigenvalues and establish conditions to be Anosov. As an application, we
also obtain a characterization of strongly convex cocompact subgroups of the
projective linear group $\mathsf{PGL}_d(\mathbb{R})$.
