Quasi-multiplier homotopes of ternary rings of operators

Hong-Wei Wang; Selim Çetin; Mehmet Gürdal; Ömer Kişi; Qing-Bo Cai; Hong-Wei Wang; Selim Çetin; Mehmet Gürdal; Ömer Kişi; Qing-Bo Cai

doi:10.3934/math.20261272

AIMS Mathematics

2026, Volume 11, Issue 10: 32369-32393. doi: 10.3934/math.20261272

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Research article

Quasi-multiplier homotopes of ternary rings of operators

1.
Fujian Provincial Key Laboratory of Data-Intensive Computing, Key Laboratory of Intelligent Computing and Information Processing, School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
2.
Department of Mathematics, Burdur Mehmet Akif Ersoy University, Burdur, Turkey
3.
Department of Mathematics, Süleyman Demirel University, Isparta 32260, Turkey
4.
Department of Mathematics, Bartın University, Bartın, Turkey

Received: 08 August 2026 Revised: 14 September 2026 Accepted: 24 September 2026 Published: 08 October 2026
MSC : Primary 47L25, 46L07, Secondary 46H10, 47A60, 46L08

We study associative products $ x\star_z y = xzy $ on a ternary ring of operators $ X $, where $ z\in X^* $ is contractive. Completely isometric isomorphisms are characterized by the orbit of the parameter under ternary isomorphisms. For every such parameter, we compute the Jacobson radical and show that it has cube zero. For closed-range parameters, the semisimple quotient is completely boundedly isomorphic to a $ C^* $-corner. For nonzero closed-range parameters on $ \mathcal B(H, K) $, the existence of a bounded algebra isomorphism is equivalent to the existence of a completely bounded one. These isomorphism classes are determined by the dimensions of the range, kernel, and cokernel. We also obtain an explicit divided-difference functional calculus and extend the closed-range results to adjointable operators on Hilbert $ C^* $-modules.
- ternary ring of operators,
- quasi-multiplier,
- operator algebra,
- Jacobson radical,
- completely bounded isomorphism
Citation: Hong-Wei Wang, Selim Çetin, Mehmet Gürdal, Ömer Kişi, Qing-Bo Cai. Quasi-multiplier homotopes of ternary rings of operators[J]. AIMS Mathematics, 2026, 11(10): 32369-32393. doi: 10.3934/math.20261272

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Abstract

We study associative products $ x\star_z y = xzy $ on a ternary ring of operators $ X $, where $ z\in X^* $ is contractive. Completely isometric isomorphisms are characterized by the orbit of the parameter under ternary isomorphisms. For every such parameter, we compute the Jacobson radical and show that it has cube zero. For closed-range parameters, the semisimple quotient is completely boundedly isomorphic to a $ C^* $-corner. For nonzero closed-range parameters on $ \mathcal B(H, K) $, the existence of a bounded algebra isomorphism is equivalent to the existence of a completely bounded one. These isomorphism classes are determined by the dimensions of the range, kernel, and cokernel. We also obtain an explicit divided-difference functional calculus and extend the closed-range results to adjointable operators on Hilbert $ C^* $-modules.

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