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arXiv · 1907.05835

A quantum metric on the Cantor Space

Konrad Aguilar·Alejandra López
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Abstract

The first author and Latr\'emoli\`ere had introduced a quantum metric (in the sense of Rieffel) on the algebra of complex-valued continuous functions on the Cantor space. We show that this quantum metric is distinct from the quantum metric induced by a classical metric on the Cantor space. We accomplish this by showing that the seminorms induced by each quantum metric (Lip-norms) are distinct on a dense subalgebra of the algebra of complex-valued continuous functions on the Cantor space. In the process, we develop formulas for each Lip-norm on this dense subalgebra and show these Lip-norms agree on a Hamel basis of this subalgebra. Then, we use these formulas to find families of elements for which these Lip-norms disagree.

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BibTeXRIS

Konrad Aguilar, Alejandra López. 2019-07-12. A quantum metric on the Cantor Space. https://doi.org/10.2140/involve.2023.16.737

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