Norm estimates for multiplication operators in Hilbert algebras
The author shows that, for the bilinear operator defined by the operation of multiplication in an arbitrary associative algebra \(V\) with unit \(e_0\) over \(\mathbb{R}\) or \(\mathbb{C}\), the infimum of its norm with respect to all scalar products in this algebra (with \(\|e_0\|=1)\) is either infinite or at most \(\sqrt{4/3}\). He presents sufficient conditions for this bound to be not less than \(\sqrt{4/3}\).
scientific article; zbMATH DE number 1928283