Hilbert norms for graded algebras

Details Hilbert norms for graded algebras Hilbert norms for graded algebras

1997-12-15

arxiv.org/abs/funct-an/9712005v2

Proc. Amer. Math. Soc. 128 (1999) 1647-1653

Mathematics

Operator Algebras

8 pages, extended introduction and list of references

Scientific paper

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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