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MR697058 (84e:47026) 47A62 (47B10)
Weiss, Gary An extension of the Fuglede commutativity theorem modulo the Hilbert-Schmidt class to operators of the form $\sum M\sb{n}XN\sb{n}$. Trans. Amer. Math. Soc. 278 (1983), no. 1, 1–20.
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