Keling, E dan F gacha bo'lgan chiziqli operatorlar to'plamini B ((E,F) bilan ifodalantsak. B ((E,F) ni norm operatoriga nisbatan to'liqligini ko'rsatish uchun B (Tn) ni B ((E,F) da Cauchy ketma-ketligi bo'lsin. Keyin ε > 0, shunday N mavjud bo'lsinki, barcha n,m ≥ N uchun bizda bo'ladiTn - Tm = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx = yx =
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