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arXiv · 2412.04824

Taylor spectrum of a Banach module over the quantum plane

Anar Dosi
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Abstract

In the paper we investigate the joint spectra of Banach space representations of the quantum q-plane called Banach q-modules. Based on the transversality relation from the topological homology of the trivial modules versus given a left Banach q-module, we introduce the joint (essential) spectra of a Banach q-module. In particular, we have the well defined Taylor joint spectrum of a Banach q-module. The noncommutative projection q-property is proved for the Taylor spectrum, which stands out the conventional projection property in the commutative case. It is provided the key examples of the Banach q-modules, which do not possesses nether forward nor backward projection properties.

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Anar Dosi. 2024-12-06. Taylor spectrum of a Banach module over the quantum plane. https://arxiv.org/abs/2412.04824

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