Certain Invertible Operator-Block Matrices Induced by C*-Algebras and Scaled Hypercomplex Numbers

Authors

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

Document Type

Article

Publication Date

10-21-2023

Abstract

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.

Comments

This article was originally published in Research in the Mathematical Sciences, volume 10, in 2023. https://doi.org/10.1007/s40687-023-00411-0

Recommended Citation

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

Peer Reviewed

1

Copyright

The authors

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This work is licensed under a Creative Commons Attribution 4.0 License.