Beckenbach was famous for his work on inequalities and for this subject organized three Oberwolfach seminars (in 1976, 1978, and 1981).
In 1951/1952 he was an assistant at the Mathematical Research Institute at Oberwolfach and from 1952 to 1954 at the University of Munich.
During 1964-1967 at the Forschungsinstitut für Mathematik at the ETH in Zurich he worked on the Category of Categories and was especially influenced by Pierre Gabriel's seminars at Oberwolfach on Grothendieck's foundation of algebraic geometry.