Theory of the (m,σ)-general functions over infinite-dimensional Banach spaces

In this paper, we introduce some functions, called (m, σ)-general, that generalize the (m, σ)-standard functions and are defined in the infinite-dimensional Banach space E_I of the bounded real sequences {xn}n∈I, for some subset I of N*. Moreover, we recall the main results about the differentiation theory over E_I, and we expose some properties of the (m, σ)-general functions. Finally, we study the linear (m, σ)-general functions, by introducing a theory that generalizes the standard theory of the m × m matrices.