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Hilbert norms for graded algebras

Authors: Joachim Kupsch and Oleg G. Smolyanov
Journal: Proc. Amer. Math. Soc. 128 (2000), 1647-1653
MSC (2000): Primary 16W50, 16W55; Secondary 46C05, 46H25
Published electronically: November 24, 1999
MathSciNet review: 1707524
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Joachim Kupsch
Affiliation: Fachbereich Physik der Universität Kaiserslautern, D-67663 Kaiserslautern, Germany

Oleg G. Smolyanov
Affiliation: Faculty of Mechanics and Mathematics, Moscow State University, 119899 Moscow, Russia

Received by editor(s): February 20, 1998
Received by editor(s) in revised form: August 3, 1998
Published electronically: November 24, 1999
Additional Notes: The second author was supported in part by the Deutsche Forschungsgemeinschaft (DFG) and by the Russian Fund of Fundamental Research
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society

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