Hilbert norms for graded algebras

Kupsch, Joachim; Smolyanov, Oleg

doi:10.1090/S0002-9939-99-05569-0

Hilbert norms for graded algebras
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by Joachim Kupsch and Oleg G. Smolyanov PDF

Proc. Amer. Math. Soc. 128 (2000), 1647-1653 Request permission

Abstract:

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.

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