19 citations · 24 across the 9 of their papers we have counts for
9 papers
Octonionic isometric isomorphisms and partial isometry
Qinghai Huo, Guangbin Ren, Zhenghua Xu
Very recently, two new notions of para-linear mappings and weak associative orthonormal bases were introduced in octonionic functional analysis, which have been proved to be powerf…
Octonionic Riesz-Dunford functional calculus
Qinghai Huo, Guangbin Ren, Irene Sabadini +1
The Riesz-Dunford functional calculus over the algebra of octonions, denoted by , has long been an open problem due to the nonassociativity of octonions. Two core obsta…
Octonionic Para-linear Self-Adjoint Operators and Spectral Decomposition
Qinghai Huo, Guangbin Ren, Irene Sabadini
This paper presents a groundbreaking advancement in the theory of operators defined on octonionic Hilbert spaces, successfully resolving a fundamental challenge that has persisted…
Monogenic functions over real alternative *-algebras: fundamental results and applications
Qinghai Huo, Guangbin Ren, Zhenghua Xu
The concept of monogenic functions over real alternative -algebras has recently been introduced to unify several classical monogenic (or regular) functions theories in hyperc…
Non-associative Categories of Octonionic Bimodules
Qinghai Huo, Guangbin Ren
Category is put to work in the non-associative realm in the article. We focus on a typical example of non-associative category. Its objects are octonionic bimodules, morphisms are…
Structure of octonionic Hilbert spaces with applications in the Parseval equality and Cayley-Dickson algebras
Qinghai Huo, Guangbin Ren
Contrary to the simple structure of the tensor product of the quaternionic Hilbert space, the octonionic situation becomes more involved. It turns out that an octonionic Hilbert sp…
Para-linearity as the nonassociative counterpart of linearity
Qinghai Huo, Guangbin Ren
In an octonionic Hilbert space , the octonionic linearity is taken to fail for the maps induced by the octonionic inner products, and it should be replaced with the octonionic p…
Octonionic bimodule
Qinghai Huo, Guangbin Ren
The structure of octonionic bimodules is formulated in this paper. It turns out that every octonionic bimodule is a tensor product, the category of octonionic bimodules is isomorph…
Classification of left octonion modules
Qinghai Huo, Yong Li, Guangbin Ren
It is natural to study octonion Hilbert spaces as the recently swift development of the theory of quaternion Hilbert spaces. In order to do this, it is important to study first its…