Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589636 | Journal of Functional Analysis | 2016 | 19 Pages |
Abstract
We show that the spectral measure of any non-constant non-commutative polynomial evaluated at a non-commutative n-tuple cannot have atoms if the free entropy dimension of that n-tuple is n (see also work of Mai, Speicher, and Weber). Under stronger assumptions on the n-tuple, we prove that the spectral measure of any non-constant non-commutative polynomial function is not singular, and measures of intervals surrounding any point may not decay slower than polynomially as a function of the interval's length.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ian Charlesworth, Dimitri Shlyakhtenko,