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On a class of bicomplex sequences. (English) Zbl 1213.30086

Summary: We consider a class \(\mathcal B\) of bicomplex sequences, i.e. sequences of bicomplex numbers. A modified Banach algebraic structure is provided to \(\mathcal B\) which is not a division algebra. Invertible and quasi-invertible elements in \(\mathcal B\) are characterised. By defining a suitable involution \(\mathcal B\) becomes a modified Banach\({}^ *\) algebra, which is not a \(\mathrm{B}^ *\) algebra. Topological zero divisors in \(\mathcal B\) are studied.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
46H99 Topological algebras, normed rings and algebras, Banach algebras
46K05 General theory of topological algebras with involution
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