Differentiability of scalar functions applied to Hermitian operators - a Fourier transform approach
| dc.creator | Levy, Eliahu | |
| dc.date | 2006-02-09 | |
| dc.date.accessioned | 2026-07-07T07:03:15Z | |
| dc.date.available | 2026-07-07T07:03:15Z | |
| dc.description | Let g be a (say, sufficiently differentiable) function on the reals. One knows how to apply g to Hermitian elements A of a C* algebra. Yet the question of differentiability of the mapping A to g(A) is not trivial, since in general "A and dA do not commute". However, since this mapping depends linearly on g, one can, via Fourier transform, reduce the case of general g to the case of the exponential function. For the latter one has an explicit formula for the n-th derivative (more complicated than in the scalar case - still "A and dA do not commute"). In this way one bounds the norm of the n-th derivative of (A to g(A)) on the r-ball by a Sobolev norm involving the (n+1)-th derivative of g on [-r,r]. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0602184 | |
| dc.identifier | http://arxiv.org/abs/math/0602184 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108903 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46G05, 47B15 | |
| dc.title | Differentiability of scalar functions applied to Hermitian operators - a Fourier transform approach | |
| dc.type | text |