 Let "H" be a Hilbert space.A bounded operator "A" on "H" is said to be subnormal if "A" has a normal extension.In other words, "A" is subnormal if there exists a Hilbert space "K" such that "H" can be embedded in "K" and there exists a normal operator "N" of the form

for some bounded operators

Every normal operator is subnormal by definition, but the converse is not true in general.