Let be a von Neumann algebra, let be a -automorphism of , and let be the crossed product determined by and . In this paper, considering the Cholesky decomposition for a positive operator in , we give a factorization theorem for positive operators in with respect to analytic crossed product determined by and . And we give a necessary and sufficient condition that every positive operator in can be factored by the form , where belongs to .
Tomoyoshi OHWADA. Kichi-Suke SAITO. "Factorization in analytic crossed products." J. Math. Soc. Japan 54 (1) 21 - 33, January, 2002. https://doi.org/10.2969/jmsj/1191593953