算子摄动与谱值映射的连续性

讨论 Hibert空间上有界线性算子摄动和谱值映射的连续性问题 .得到 σk(.)一类子集上半连续的充要条件和 H∞∞ (.)连续的充要条件 ,推广了文 [7]主要结果 .     

Test elements and the retract theorem for monounary algebras

The term “Retract Theorem” has been applied in literature in connection with group theory. In the present paper we prove that the Retract Theorem is valid (i) for each finite structure, and (ii) for each monounary algebra. On the other hand, we show that this theorem fails to be valid, in general, for algebras of the form A=(A, F), where each f ∈ F is unary and card F > 1. This work was supported by grant VEGA 1/0423/03 and by Science and Technology Assistance Agency under the contract No.APVT-20-004104.     

On Ocneanu's theory of double triangle algebras for subfactors and classification of irreducible connections on the Dynkin diagrams

We give an exposition of Ocneanu's theory of double triangle algebras for subfactors and its application to the classification of irreducible bi-unitary connections on the Dynkin diagrams _An$A_n$, _Dn$D_n$, _E6$E_6$, _E7$E_7$ and _E8$E_8$. More precisely, we give a detailed proof of the complete classification of irreducible K–L$K–L$ bi-unitary connections up to gauge choice, where K and L   represent the two horizontal graphs which are among the A–D–E$A–D–E$ Dynkin diagrams. The result also provides a simple proof of the flatness of _D2n$D_{2n}$, _E6$E_6$ and _E8$E_8$ connections as well as an easy computation of the flat part of _E7$E_7$ as an application.