It is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux, arise naturally in the study of topological groups with no small subgroups, of Banach or normed algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or normed algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given, and other related results are proved.

Let D(A) be the domain of an m-accretive operator A on a Banach space E. We provide sufficient conditions for the closure of D(A) to be convex and for D(A) to coincide with E itself. Several related results and pertinent examples are also included.

By means of the Pucci operator, we construct a function ${{u}_{0}}$, which plays an essential role in our considerations, and give the existence and regularity theorems for the bounded viscosity solutions of the generalized Dirichlet problems of second order fully nonlinear elliptic equations on the general bounded domains, which may be irregular. The approximation method, the accretive operator technique and the Caffarelli's perturbation theory are used.