Geodesic
A characterization of subnormal operators
Glasgow mathematical journal, Tome 25 (1984) no. 1, pp. 99-101

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In this note a characterization of subnormality of operators on Hilbert space is given. The characterization is in terms of a sequence of polynomials in the operator and its adjoint reminiscent of the binomial expansion in commutative algebras. As such no external Hilbert spaces are needed, nor is it necessary to introduce forms dependent on arbitrary sequences of vectors from the Hilbert space. 
Lambert, Alan. A characterization of subnormal operators. Glasgow mathematical journal, Tome 25 (1984) no. 1, pp. 99-101. doi: 10.1017/S0017089500005474
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