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Some Fundamental Theorems of Functional Analysis with Bicomplex and Hyperbolic Scalars

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Abstract

We discuss some properties of linear functionals on topological hyperbolic and topological bicomplex modules. The hyperbolic and bicomplex analogues of the uniform boundedness principle, the open mapping theorem, the closed graph theorem and the Hahn Banach separation theorem are proved.

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Acknowledgements

The authors would like to thank the referees and the Professor Rafal Ablamowicz for their helpful comments and valuable suggestions for improving the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Govt. M. A. M. College, Jammu, J&K, 180 006, India

    Heera Saini

  2. Department of Mathematics, University of Jammu, Jammu, 180 006, India

    Aditi Sharma & Romesh Kumar

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  1. Heera Saini
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Correspondence to Romesh Kumar.

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Communicated by Irene Sabadini

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Saini, H., Sharma, A. & Kumar, R. Some Fundamental Theorems of Functional Analysis with Bicomplex and Hyperbolic Scalars. Adv. Appl. Clifford Algebras 30, 66 (2020). https://doi.org/10.1007/s00006-020-01092-6

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