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

Abstract

In this paper, we introduce some functions, called (m; σ)- general, that generalize the (m; σ)-standard functions and are dfined in the infinite-dimensional Banach space EI of the bounded real sequences fxngn2I, for some subset I of N*. Moreover, we recall the main results about the differentiation theory over EI , 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 x m matrices.