1. The references areF. Riesz (Acta Math..,41 (1918), pp. 71–98),T. H. Hildebrandt (Acta Math.,51 (1928), pp. 311–318) andJ. Schauder (Studia Math.,2 (1930), pp. 183–196). A later account is given byS. Banach,Théorie des opérations linéaires (Warsaw, 1932), pp 151–164.
2. Ф. В. Аткинсон Нормальная раврешимость линеиньIх уравнений в нормированньIх пространствах, Матем. сборник,28 (70) (1951), pp. 3–14.
3. I depart here fromBanach's notation, in which this equation would have been written $$\bar T$$ (l)=0
4. Cases in which they are not necessarily equal formed the subject of my abovecited paper.
5. Similar procedures have been employed byС. М. Никольский Известия А. Н. СССР, сер. матем.,7, No. 3 (1943), pp. 147–166, and by myself in my paper mentioned above. See alsoS. Banach, loc. cit.Théorie des opérations linéaires (Warsaw, 1932), pp 151–164.