Rapid decay and functional calculus in ${\rm C}^*$-probability spaces

Felipe Flores

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arXiv · 2609.00452

Rapid decay and functional calculus in ${\rm C}^*$-probability spaces

Felipe Flores

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Abstract

Let $(A,\rho)$ be a tracial ${\rm C}^*$-probability space with the rapid decay property relative to a filtration $L$. We show that the associated Sobolev algebra $H_L^{\infty}(A,\rho)$ is closed under the smooth functional calculus of $A$. Some consequences include norm estimates, the ideal separation property, and the fact that the inclusion $H_L^{\infty}(A,\rho)\subset A$ induces an isomorphism in $K$-theory.

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Felipe Flores. 2026-08-31. Rapid decay and functional calculus in ${\rm C}^*$-probability spaces. https://arxiv.org/abs/2609.00452

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