62 research outputs found
Approximation of the spectral action functional in the case of -compact resolvents
We establish estimates and representations for the remainders of Taylor
approximations of the spectral action functional on
bounded self-adjoint perturbations, where is a self-adjoint operator with
-compact resolvent in a semifinite von Neumann algebra and belongs to
a broad set of compactly supported functions including -times differentiable
functions with bounded -th derivative. Our results significantly extend
analogous results in \cite{SkAnJOT}, where was assumed to be compactly
supported and -times continuously differentiable. If, in addition, the
resolvent of belongs to the noncommutative -space, stronger
estimates are derived and extended to noncompactly supported functions with
suitable decay at infinity.Comment: 13 page
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