Abstract
There are discussed the two types of norms on bicomplex modules: the norms with real values and those with values in non–negative hyperbolic numbers. It turns out that hyperbolic valued norms are better compatible with the structure of bicomplex modules. In particular, the bicomplex valued inner products generate in a usual way: hyperbolic, not real, valued norms. As an example, the ring of biquaternions (complex quaternions) is treated as a bicomplex module.
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R. Gervais Lavoie, L. Marchildon, D. Rochon, Infinite-dimensional bicomplex Hilbert spaces. Ann. Funct. Anal. 1(2), 75–91 (2010)
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Alpay, D., Luna-Elizarrarás, M.E., Shapiro, M., Struppa, D.C. (2014). Norms and Inner Products on \(\mathbb B\mathbb C\)-Modules. In: Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-05110-9_4
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DOI: https://doi.org/10.1007/978-3-319-05110-9_4
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