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.References
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Additional Information
- Joachim Kupsch
- Affiliation: Fachbereich Physik der Universität Kaiserslautern, D-67663 Kaiserslautern, Germany
- Email: kupsch@physik.uni-kl.de
- Oleg G. Smolyanov
- Affiliation: Faculty of Mechanics and Mathematics, Moscow State University, 119899 Moscow, Russia
- Email: smolian@nw.math.msu.su
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1647-1653
- MSC (2000): Primary 16W50, 16W55; Secondary 46C05, 46H25
- DOI: https://doi.org/10.1090/S0002-9939-99-05569-0
- MathSciNet review: 1707524