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.
Access this article
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Similar content being viewed by others
References
Davison, T. M. K.,Jordan derivations and quasi-bilinear forms. Comm. Algebra12 1 (1984), 23–32.
Kurepa, S.,The Cauchy functional equation and scalar product in vector spaces. Glas. Mat. Ser. III19 (1964), 23–35.
Kurepa, S.,Quadratic and sesquilinear functionals. Glas. Mat. Ser. III (1965), 79–92.
Vrbova, P.,Quadratic functionals and bilinear forms. Casopis Pest. Mat.98 (1973), 159–161.
Vukman, J.,A result concerning additive functions in hermitian Banach *-algebras and an application. Preprint.
Zariski, O. andSammuel, P.,Commutative algebra. D. Van Nostrand Company, 1958.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Šemrl, P. On quadratic and sesquilinear functionals. Aeq. Math. 31, 184–190 (1986). https://doi.org/10.1007/BF02188187
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02188187