The implications of the positivity constraint on the presently unknown pola
rized structure function of the photon, g(1)(gamma)(x, Q(2)), are studied i
n detail. In particular the non-trivial consequences of this constraint, /g
(1)(gamma)(x, Q(2))/ less than or equal to F-1(gamma)(x, Q(2)), in the next
-to-leading order analysis of g(1)(gamma) are pointed out by employing appr
opriate (DIS) factorization schemes related to g(1)(gamma) and rather F-1(g
amma) (rather than to F-2(gamma)). (C) 2001 Elsevier Science B.V. All right
s reserved.