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arXiv · 2301.09513

Approximation of the spectral action functional in the case of $\tau$-compact resolvents

Arup Chattopadhyay·Chandan Pradhan·Anna Skripka
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Abstract

We establish estimates and representations for the remainders of Taylor approximations of the spectral action functional $V\mapsto\tau(f(H_0+V))$ on bounded self-adjoint perturbations, where $H_0$ is a self-adjoint operator with $\tau$-compact resolvent in a semifinite von Neumann algebra and $f$ belongs to a broad set of compactly supported functions including $n$-times differentiable functions with bounded $n$-th derivative. Our results significantly extend analogous results in \cite{SkAnJOT}, where $f$ was assumed to be compactly supported and $(n+1)$-times continuously differentiable. If, in addition, the resolvent of $H_0$ belongs to the noncommutative $L^n$-space, stronger estimates are derived and extended to noncompactly supported functions with suitable decay at infinity.

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Arup Chattopadhyay, Chandan Pradhan, Anna Skripka. 2023-01-23. Approximation of the spectral action functional in the case of $\tau$-compact resolvents. https://arxiv.org/abs/2301.09513

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