与Misra-Prigogine-Courbage不可逆理论相关的Rigged Hilbert空间
Rigged Hilbert Spaces associated with Misra-Prigogine-Courbage Theory of Irreversibility
摘要：
证明了在Misra-Prigogine-Courbage不可逆性理论中，如果使用内部时间超算子，固定它的非幺正变换$Λ$，就等于改变相应的Hilbert-Liouville空间.更精确地说，证明了任何$Λ$都决定了Liouville空间$\QTR{cal}{L}$的三个标准规范：第一个规范规范是一个Hilbert空间，其范数大于$\QTR{cal}{L}$的相对规范，第二个规范是一个$σ$空间，如果$Λ$是紧的，则它是一个Köthe空间，如果$Λ$具有某些核性质，则它是一个核空间;第三个是一个更小的$σ$ -希尔伯特空间，它具有更强的拓扑，如果$Λ^{n}$是Hilbert-Schmidt，则它是核的。反之亦然：任何这种类型的装备，起源于一个具有内部时间超算子的动力系统，以规范的方式定义了一个$Λ$。
英文摘要：
It is proved that, in the Misra-Prigogine-Courbage Theory of Irreversibility using the Internal Time superoperator, fixing its associated non-unitary transformation $Λ$, amounts to rigging the corresponding Hilbert-Liouville space. More precisely, it is demonstrated that any $Λ$ determinates three canonical riggings of the Liouville space $\QTR{cal}{L}$: a first one with a Hilbert space with a norm greater than the relative one from $\QTR{cal}{L}$; a second one with a $σ$-Hilbertian space, which is a Köthe space if $Λ$ is compact and is a nuclear space if $Λ$ has certain nuclear properties; and finally a third one with a smaller $σ$-Hilbertian space with a still stronger topology which is nuclear if $Λ^{n}$ is Hilbert-Schmidt, for some positive integer n. Viceversa: any rigging of this type, originated in a dynamical system having an Internal Time superoperator, defines a $Λ$ in a canonical way.
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