Some estimates of action constants and related parameters

In this paper, we continue investigation of an action constant λA(V) introduced in [1–3]. In particular, we show that, if n is the dimension of V, then λA(V) ≤ θ(A)√n, which is the generalization of the well-known estimate λI(V) ≤ √n. We then proceed to compare the estimates for λA(V) and λI(V) for a variety of two-dimensional spaces. These estimates are obtained with the extensive use of computer interaction.