Geodesic
Two conditions for subnormality of unbounded operators
Glasgow mathematical journal, Tome 43 (2001) no. 1, pp. 23-28

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We give two new sufficient conditions for unbounded Hilbert space operators to be subnormal. The first assumes that the sequence //Tnf//2 on a suitable subset of the domain is completely monotonic, the second is similar to the one given by Lambert in [3] for bounded operators and involves the sequence of binomial expansion of the real part of the operator. 
Niechwiej, Jan. Two conditions for subnormality of unbounded operators. Glasgow mathematical journal, Tome 43 (2001) no. 1, pp. 23-28. doi: 10.1017/S0017089501010035
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     title = {Two conditions for subnormality of unbounded operators},
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     year = {2001},
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     doi = {10.1017/S0017089501010035},
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