C*-dynamical rapid decay

Erik Christensen

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arXiv · 2101.08634

C*-dynamical rapid decay

Erik Christensen

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Abstract

Some well known results by Haagerup, Jolissaint and de la Harpe may be extended to the setting of a reduced crossed product of a C*-algebra A by a discrete group $G.$ We show that for many discrete groups, which include Gromov's hyperbolic groups and finitely generated discrete groups of polynomial growth, an inequality of the form $$\|X\| \leq C \sqrt{\sum_{g \in G} (1+|g|)^4 \|X_g\|^2 } $$ holds for any finitely supported operator $X$ in the reduced crossed product.

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Erik Christensen. 2021-01-21. C*-dynamical rapid decay. https://arxiv.org/abs/2101.08634

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