... M˘a.t kh´ac, do phi´ˆem h`am c’ua ¯d`ˆe b`ai liˆen tu.c nˆenlimn→∞Axn, u = Ax, u (ii) 3∀u ∈ X. T`’u (i) v`a (ii) , ta suy ray, u = Ax, u ⇔ y − Ax, u = 0, ∀u ∈ X⇔ y − Ax = 0 ⇔ y = Ax.Do ¯d´o ... c’o s’’o c’ua khˆong gian Hilbert X v`aPnx =nk=1x, ekek, x ∈X, n = 1, 2, . . .l`a d˜ay ph´ep chii´ˆeu tr’u.c giao. Ch´’ung minh r`˘ang d˜ay {Pn}nhˆo.i tu.¯di’ˆem ¯d´ˆen to´an t’’u ¯d`ˆongnh´ˆat...