  This paper presents a solution to a problem from superanalysis about the
existence of Hilbert-Banach superalgebras. Two main results are derived: 1)
There exist Hilbert norms on some graded algebras (infinite-dimensional
superalgebras included) with respect to which the multiplication is continuous.
2) Such norms cannot be chosen to be submultiplicative and equal to one on the
unit of the algebra.
