Let M be a von Neumann algebra, let α be a *-automorphism of M, and let M\
times
α\bm{Z} be the crossed product determined by M and α. In this paper, considering the Cholesky decomposition for a positive operator in M\
times
α\bm{Z}, we give a factorization theorem for positive operators in M\
times
α\bm{Z} with respect to analytic crossed product M\
times
α\bm{Z}
+ determined by M and α. And we give a necessary and sufficient condition that every positive operator in M\
times
α\bm{Z} can be factored by the form A
*A, where A belongs to M\
times
α\bm{Z}
+∩(M\
times
α\bm{Z}
+)
-1.
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