Dalla teoria delle funzioni all'analisi funzionale: il carteggio Arzelà-Volterra

In this paper I present a small fragment out of the extraordinary Nachlass of Vito Volterra (1860–1940). Since the corresponding collection of Cesare Arzelà (1847–1912) is not known, we have 96 letters from him and drafts or notes of 6 of Volterra’s replies, covering 30 years to Arzelà’s death. 81 items are given and discussed here, of which the principal mathematical themes deal with the emergence, from Weierstrass’ tradition of real-variable analysis (uniform convergence of series, the foundations of Dirichlet’s principle, and the like), of functional analysis—“functions of lines” in Volterra’s phrase.