Abstract
The problem of representability of quadratic functionals (acting on modules over unital complex ∗-algebras), by sesquilinear forms, is generalized by weakening the homogeneity equation. The corresponding representation theorem can be considered as a generalization of (the original form of) the classical Jordan–von Neumann characterization of complex inner product spaces.
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Dedicated to the memory of Professor Svetozar Kurepa
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Ilišević, D. A generalization of the original Jordan–von Neumann theorem. Acta Math Hung 132, 387–400 (2011). https://doi.org/10.1007/s10474-011-0075-5
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DOI: https://doi.org/10.1007/s10474-011-0075-5
Key words and phrases
- quadratic functional
- homogeneity equation
- sesquilinear form
- ∗-ring
- complex ∗-algebra
- ideal
- (bi)module
- complex vector space
- Jordan derivation