On Gram's determinant in 2-inner product spaces (Q2770396)

The theory of 2-inner product spaces has been extensively studied in a book by \textit{Y. J. Cho}, \textit{P. C. S. Lin}, \textit{S. S. Kim} and \textit{A. Misiak} [Theory of 2-inner product spaces, Nova Science Publishers, New York (2001; Zbl 1016.46002)]. Here, by analogy with the 1-inner product case (i.e., prehilbertian spaces), the authors introduce the concept of a Gram determinant of these spaces. The most important results, such as Gram's inequality, Parseval's identity, Bessel's inequality, Cauchy-Schwarz's inequality, etc., are stated and proved in terms of 2-inner products.