PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 51(65), pp. 81--86 (1992)
Sesquilinear and quadratic forms on modules over $*$-algebras
C.-S. LinDepartment of Mathematics, Bishop's University, Lennoxville, P.Q. J1M1Z7, Canada
Abstract: We define three new quadratic forms on a module over a $*$-algebra. It is shown that for each quadratic form with a certain property, there exists a sesquilinear form such that both forms are equal to each other. The converse statement is also valid. So far as application is concerned this result enables us to form new characterization formulas for an inner product space if we restrict attention to normed linear spaces.
Classification (MSC2000): 46H05, 46K05, 46C10
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