Schatten classes on noncommutative tori: Kernel conditions

Ruzhansky, Michael; Zeng, Kai

doi:10.1090/proc/17253

Schatten classes on noncommutative tori: Kernel conditions
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by Michael Ruzhansky and Kai Zeng;

Proc. Amer. Math. Soc. 153 (2025), 2467-2479

DOI: https://doi.org/10.1090/proc/17253

Published electronically: April 3, 2025

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Abstract:

In this note, we give criteria on noncommutative integral kernels ensuring that integral operators on quantum torus belong to Schatten classes. With the engagement of a noncommutative Schwartz’ kernel theorem on the quantum torus, a specific test for Schatten class properties of bounded operators on the quantum torus is established.

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Proceedings of the American Mathematical Society

Schatten classes on noncommutative tori: Kernel conditions
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Abstract: