Bartle-Graves theorem
Bartle-Graves theorem - in functional analysis, the theorem proved by R. G. Bartle and L.M. Graves in 1952, which says that for every surreal linear operator T & # x003A; X & # x2192; Y {\displaystyle T\colon X\to Y} there is such a continuous function between Banach spaces g & # x003A; Y & # x2192; X , {\displaystyle g\colon Y\to X,} that T & # x2218; g = i d Y . {\displaystyle T\circ g={\rm {id}}_{Y}.} The thesis of the theorem does not occur for the two-line surreal mappings. wiki