Author

Jun-Sheng Fang

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Preprint Oct 2026

Strongly irreducible operators, $K_0$-groups, and Jones indices in the hyperfinite type $\mathrm{II}_1$ factor

In this paper, we study the strong irreducibility of a class of operators associated with irrational rotation algebras in the hyperfinite type $\mathrm{II}_1$ factor $\mathcal R$. By developing weighted shift models for their relative commutants, we obtain $K_0$ calculations and splitting criteria for direct sums. In p...

Jun-Sheng Fang, Chun-Lan Jiang, Ming-Hui Ma et al. · 0 citations

Preprint Oct 2026

The invariant subspace problem and Rosenblum operators II

Let $\mathcal{H}$ be the separable, infinite-dimensional complex Hilbert space. In the first paper of this series, we introduced, by means of the Rosenblum operators, the shift representation operators $K_x=\sum_{n=0}^{\infty}T^nx\otimes e_n$, which relate an operator $T$ with $r(T)<1$ to the unilateral shift $S$ and r...

Jun-Sheng Fang, Bing-Zhe Hou, Chun-Lan Jiang et al. · 0 citations