Abstract
LetX be a leftA-module, whereA is either a complex Banach *-algebra with an identity element or the field of quaternions. The main result of this note is that forQ, anA-quadratic functional defined onX, there exists a sesquilinear functionalB such thatB(x,x)=Q(x) holds for allxεX.
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Šemrl, P. On quadratic and sesquilinear functionals. Aeq. Math. 31, 184–190 (1986). https://doi.org/10.1007/BF02188187
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DOI: https://doi.org/10.1007/BF02188187