Toeplitz matrices acting on the ℓ²-space of an imprimitivity bimodule

Abadie, Beatriz

doi:10.1090/proc/15746

Toeplitz matrices acting on the $\ell ^2$-space of an imprimitivity bimodule
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by Beatriz Abadie

Proc. Amer. Math. Soc. 150 (2022), 1269-1278

DOI: https://doi.org/10.1090/proc/15746

Published electronically: January 5, 2022

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Abstract:

We give a definition of Toeplitz matrix acting on the $\ell ^2$-space of an imprimitivity bimodule $X$ over a $C^*$-algebra $A$. We characterize the set of Toeplitz matrices as the closure in a certain topology of the image of the left regular representation of the crossed product $A\rtimes X$.

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