The establishment of functional analysis
This comprehensive survey of functional analysis treats its sources and development up to the publication of Banach's book. Once reasonably clear notions of function and space were in place, the basic ideas were developed first by Italian and slightly later by French investigators. Calculus of variations and integral equations provided the occasion to hone and apply the tools of abstract analysis. The work of Hilbert and his associates as well as of Frédéric Riesz is discussed in detail. A brief survey of early point set topology leads into an account of Banach's work and the fundamental theorems of functional analysis. The paper concludes with a discussion of papers delivered at Bologna in 1928, research into fixed point and ergodic theory and the contributions of von Neumann and M. H. Stone.
scientific article; zbMATH DE number 3875196