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.
