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Hilbert norms for graded algebras

Joachim Kupsch·Oleg G. Smolyanov
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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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Joachim Kupsch, Oleg G. Smolyanov. 2000-12-13. Hilbert norms for graded algebras. https://arxiv.org/abs/funct-an/9712005

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