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Line 53: For a counter example that shows the converse is not true, consider again the unilateral shift ''A''. The operator ''B'' = ''A'' + ''s'' for some scalar ''s'' remains subnormal. But if ''B'' is quasinormal, a straightforward calculation shows that ''AA = AA'', which is a contradiction. [[Category:Operator theory]]

Subnormal operator: Difference between revisions