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Jiang Lining

Publications and source records attributed to Jiang Lining.

5 recordsLinked to original sources
arXiv2025

Two tuples of noncommutative Orlicz sequence spaces and some geometry properties

The primary contribution of this study lies in proposing a new concept termed $2$-tuples of noncommutative Orlicz sequence spaces $\bigoplus\limits_{j=1}^{2}S_{\varphi_{j},p}$, where $S_{\varphi_{j}}$ denotes a noncommutative Orlicz sequence space. By leveraging the three-line theorem, we establish the Riesz-Thorin interpolation theorem for $\bigoplus\limits_{j=1}^{2}S_{\varphi_{j},p}$. As applications, we derive bound for the nonsquare and von Neumann-Jordan constant of noncommutative Orlicz space $S_{\varphi_{s}} (0<s\leq1)$, where $\varphi_{s}$ is an intermediate function.

math.FA↗
arXiv2015

Jones type basic construction on field algebras of $G$-spin models

Let $G$ be a finite group. Starting from the field algebra ${\mathcal{F}}$ of $G$-spin models, one can construct the crossed product $C^*$-algebra ${\mathcal{F}}\rtimes D(G)$ such that it coincides with the $C^*$-basic construction for the field algebra ${\mathcal{F}}$ and the $D(G)$-invariant subalgebra of ${\mathcal{F}}$, where $D(G)$ is the quantum double of $G$. Under the natural $\widehat{D(G)}$-module action on ${\mathcal{F}}\rtimes D(G)$,the iterated crossed product $C^*$-algebra can be obtained, which is $C^*$-isomorphic to the $C^*$-basic construction for ${\mathcal{F}}\rtimes D(G)$ and the field algebra ${\mathcal{F}}$. Furthermore, one can show that the iterated crossed product $C^*$-algebra is a new field algebra and give the concrete structure with the order and disorder operators.

math.QA↗
arXiv2015

The construction of observable algebra in field algebra of $G$-spin models determined by a normal subgroup

Let $G$ be a finite group and $H$ a normal subgroup. Starting from $G$-spin models, in which a non-Abelian field ${\mathcal{F}}_H$ w.r.t. $H$ carries an action of the Hopf $C^*$-algebra $D(H;G)$, a subalgebra of the quantum double $D(G)$, the concrete construction of the observable algebra ${\mathcal{A}}_{(H,G)}$ is given, as $D(H;G)$-invariant subspace. Furthermore, using the iterated twisted tensor product, one can prove that the observable algebra ${\mathcal{A}}_{(H,G)}=\cdots\rtimes H\rtimes\hat{G}\rtimes H\rtimes\hat{G}\rtimes H\rtimes\cdots$, where $\hat{G}$ denotes the algebra of complex functions on $G$, and $H$ the group algebra.

math.OA↗
arXiv2015

$C^*$-index of observable algebra in the field algebra determined by a normal group

Let $G$ be a finite group and $H$ a normal subgroup. $D(H;G)$ is the crossed product of $C(H)$ and ${\Bbb C}G$ which is only a subalgebra of $D(G)$, the quantum double of $G$. One can construct a $C^*$-subalgebra ${\mathcal{F}}_{_H}$ of the field algebra $\mathcal{F}$ of $G$-spin models, such that ${\mathcal{F}}_{_H}$ is a $D(H;G)$-module algebra. The concrete construction of $D(H;G)$-invariant subalgebra ${\mathcal{A}}_{_{(H,G)}}$ of ${\mathcal{F}}_{_H}$ is given. By constructing the quasi-basis of conditional expectation $z_{_H}$ of ${\mathcal{F}}_{_H}$ onto ${\mathcal{A}}_{_{(H,G)}}$, the $C^*$-index of $z_{_H}$ is given.

math.OA↗