Toeplitz-like Operators Induced by Sliced Sections in Scaled Hypercomplex Numbers
Document Type
Article
Publication Date
8-14-2026
Abstract
In this paper, we study sectional structures embedded in the t-scaled hypercomplex numbers Ht for a scale t ∈ R. For a fixed scale t ∈ R, from the subset St consisting of a certain type of pure-imaginary t-scaled hypercomplex numbers in Ht, we sectionize Ht. We concentrate on such a section SHIt for an arbitrarily fixed imaginary It ∈ St, called the t-sliced section for It. We construct some functional vector spaces induced by SHIt over the real field R, and concentrate on one of the vector space SHIt:2 [[q]] called the SHIt -Hardy space. An interesting type of operators on SHIt:2 [[q]] is introduced and studied. Especially, we are interested in Toeplitz-like operators. Operator algebra, operator theory, and certain noncommutative-statistical data induced by such Toeplitz-like operators are characterized and analyzed.
Recommended Citation
Alpay, D., Cho, I. Toeplitz-like operators induced by sliced sections in scaled hypercomplex numbers. J Anal 34, 3521–3585 (2026). https://doi.org/10.1007/s41478-026-01162-1
Peer Reviewed
1
Copyright
Springer
Comments
This article was originally published in Journal of Analysis, volume 34, in 2026. https://doi.org/10.1007/s41478-026-01162-1
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