Matrices Induced by Scaled Hypercomplex Numbers over the Real Field R

Authors

Daniel Alpay, Chapman UniversityFollow
Ilwoo Choo, St. Ambrose UniversityFollow

Document Type

Article

Publication Date

9-13-2025

Abstract

In this paper, we construct, and study a certain type of definite, or indefinite inner product spaces over the real field R, induced by the scaled hypercomplex numbers H_t for a fixed scale t ∈ R, and some bounded operators acting on such vector spaces. In particular, we are interested in the vector spaces H^N_t consisting of all N-tuples of scaled hypercomplex numbers of H_t, and the (N x N)-matrices acting on H^N_t whose entries are from H_t, i.e., H_t-matrices, for all N ∈ N. For an arbitrarily fixed N ∈ N, we define H^N_t as a subspace of a certain functional vector space H_t:2 equipped with a well-defined definite (if t < 0), or indefinite (if t ≥ 0) inner product introduced in [6, 7, 8]. So, one can check immediately that our subspace H^N_t becomes a restricted definite, or indefinite inner product Banach space. Operator-theoretic, operator-algebraic and free-probabilistic properties of H_t-matrices are considered and characterized on H^N_t .

Comments

This article was originally published in Methods of Functional Analysis and Topology, volume 31, issue 4, in 2025. https://doi.org/10.31392/MFAT-npu26_4.2025.01

Recommended Citation

Daniel Alpay and Ilwoo Cho, Matrices Induced by Scaled Hypercomplex Numbers over the Real Field R, Methods Funct. Anal. Topology 31 (2025), no. 4, 261-309. https://doi.org/10.31392/MFAT-npu26_4.2025.01

Peer Reviewed

1

Copyright

Methods of Functional Analysis and Topology (MFAT)

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