The main purposes of this paper are (i) to enlarge scaled hypercomplex structures to operator-valued cases, where the operators are taken from a C*-subalgebra of an operator algebra on a separable Hilbert space, (ii) to characterize the invertibility conditions on the operator-valued scaled-hypercomplex structures of (i), (iii) to study relations between the invertibility of scaled hypercomplex numbers, and that of operator-valued cases of (ii), and (iv) to confirm our invertibility of (ii) and (iii) are equivalent to the general invertibility of (2×2)-block operator matrices.
Alpay, D., Cho, I. Certain invertible operator-block matrices induced by C*-algebras and scaled hypercomplex numbers. Res Math Sci 10, 47 (2023). https://doi.org/10.1007/s40687-023-00411-0
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