BANACH, STEFAN

born March 30, 1892, Krakw, Austria-Hungary [now in Poland] died Aug. 31, 1945, Lvov, Ukrainian S.S.R. Polish mathematician who founded modern functional analysis and helped develop the theory of topological vector spaces. A lecturer in mathematics at the Institute of Technology, Lvov, from 1919, Banach became a lecturer at the University of Lvov in 1922 and a full professor in 1927. He contributed to the theory of orthogonal series and made innovations in the theory of measure and integration, but his most important contribution was in functional analysis. Of his published works, his Thorie des oprations linaires (1932; Theory of Linear Operations) is the most important. Banach and his coworkers summarized the previously developed concepts and theorems of functional analysis and integrated them into a comprehensive system. Banach himself introduced the concept of normed linear spaces, which are now known as Banach spaces. He also proved several fundamental theorems in the field, and his applications of theory inspired much of the work in functional analysis for the next few decades.