An L^p-Imprimitivity Theorem for the Group of Integers

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发表日期：

2026年2月18日

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Zhen Wang,
Sen Zhu

摘要

In this paper, the authors obtain an L^p-version of Green’s Imprimitivity Theorem for the group ℤ of integers. More precisely, for X = ℤ/nℤ and the action α of ℤ on X by translation, it is proved that the full L^p-operator crossed product F^p(ℤ, X, α) is isometrically isomorphic to the spatial L^p-operator tensor product of M _n ^p and the reduced group L^p-operator algebra F _λ ^p (ℤ). This solves the L^p-imprimitivity problem raised by Phillips for the group of integers. They also prove that F^p(ℤ, X, α) is isometrically isomorphic to C(S¹, M _n ^p ) precisely when p = 2, where S¹ denotes the unit circle in the complex plane ℂ. Moreover, they determine the K-theory groups of F^p(ℤ, X, α).

An Lp-Imprimitivity Theorem for the Group of Integers

摘要

An L^p-Imprimitivity Theorem for the Group of Integers