Abstract
This chapter treats, in the bicomplex context, the basic properties of linear functionals and linear operators. The notion of boundedness is given in terms of hyperbolic valued norms, thus allowing more similarity with the classical case. The bicomplex analogs of polarization identities are presented.
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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). Linear Functionals and Linear Operators 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_5
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DOI: https://doi.org/10.1007/978-3-319-05110-9_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05109-3
Online ISBN: 978-3-319-05110-9
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