On Gram's determinant in 2-inner product spaces (Q2770396)
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scientific article; zbMATH DE number 1703234
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Gram's determinant in 2-inner product spaces |
scientific article; zbMATH DE number 1703234 |
Statements
2 December 2003
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2-inner product spaces
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Gram determinant
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On Gram's determinant in 2-inner product spaces (English)
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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.
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