Journal of Operator Theory

Volume 96, Issue 1, Summer 2026 pp. 3-53.

Block-Toeplitz-like operators induced by scaled hypercomplex numbers over the real field $\mathbb{R}$

Authors: Daniel Alpay (1), Ilwoo Cho (2)
Author institution: (1) Chapman University, Department of Mathemathics, 381 Keck Center, 1 University Dr. Orange, California, 92866, U.S.A.
(2) St. Ambrose University, Department of Mathemathics and Statistics, 421 Ambrose Hall, 518 W. Locust St., Davenport, Iowa, 52803, U.S.A.

Summary: In this paper, we consider a system of scaled hypercomplex numbers of $\mathbb{H}_{t}$ for an arbitrarily fixed scale $t\in\mathbb{R}$, and construct some functional vector spaces. In particular, we concentrate on a ``Hardy-like'' space $\mathbf{H}_{t:2}[[q]]$ in an $\mathbb{H}_{t}$-variable $q$, and investigate ``Toeplitz-like'' operators on $\mathbf{H}_{t:2}[[q]]$. Some interesting operator-theoretic and operator-algebraic properties of those operators are characterized.

DOI: http://dx.doi.org/10.7900/jot.2024.nov08.2499
Keywords: Hardy-like spaces, scaled hypercomplex, Toeplitz-like operators, con\-volution-like operator, real-adjoint, operator-action, semi-inner product, semi-norm

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