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| An Lp-Imprimitivity Theorem for the Group of Integers |
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Citation： |
Zhen WANG,,Sen ZHU.An Lp-Imprimitivity Theorem for the Group of Integers[J].Chinese Annals of Mathematics B,2026,(4):593~602 |
| Page view： 595
Net amount： 362 |
Authors： |
Zhen WANG,; Sen ZHU |
Foundation： |
the National Natural Science Foundation of China (Nos. 12201240,
12171195), the National Key Research and Development Program (No. 2020YFA0714101) and the Grant
from Hangzhou Normal University (No. 4235C50224204070). |
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| Abstract： |
n this paper, the authors obtain an Lp-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 Lp-operator crossed product F p(Z, X, α) is isometrically isomorphic to the spatial Lp-operator tensor product of Mnp and the reduced group Lp-operator algebra Fλp(Z). This solves the Lp-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, Mnp) 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). |
Keywords： |
Lp-operator crossed products Lp-operator algebras Gelfand transform K-theory |
Classification： |
47L55, 47L65, 19K99, 46J05 |
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