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A characterization of the quasi-split property for an inclusion of W * -algebras in terms of the metrically nuclear maps is established. This result extends the known characterization relative to inclusions of W * -factors. An application to type I von Neumann algebras is also presented.doi:10.1090/s0002-9939-01-06154-8 fatcat:ksas56blc5a33jirjna4bfvmdq