We extend the notion of the determinant function $\Lambda$, originally introduced by T.Fack for $\tau$-compact operators, to a natural algebra of $\tau$-measurable operators affiliated with a semifinite von Neumann algebra which coincides with that defined by Haagerup and Schultz in the finite case and on which the determinant function is shown to be submultiplicative. Application is given to Holder type inequalities via general Araki-Lieb-Thirring inequalities due to Kosaki and Han and to a Weyl-type theorem for uniform majorization.

中文翻译：

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τ 可测算子的对数次大化、统一大化和 Hölder 型不等式

我们将最初由 T.Fack 为 $\tau$-compact 算子引入的行列式函数 $\Lambda$ 的概念扩展到 $\tau$-可测算子的自然代数，该算子隶属于半有限冯诺依曼代数，与由 Haagerup 和 Schultz 在有限情况下定义的，并且行列式函数被证明是可乘的。通过 Kosaki 和 Han 引起的一般 Araki-Lieb-Thirring 不等式以及统一专业化的 Weyl 型定理，将应用应用于 Holder 型不等式。