Perturbation determinants on Banach spaces and operator differentiability for Hirsch functional calculus
Functional Analysis
2019-09-04 v4
Abstract
We consider a perturbation determinant for pairs of nonpositive (in a sense of Komatsu) operators on Banach space with nuclear difference and prove a generalization of the important formula for the logarithmic derivative of this determinant. To this end the Frechet differentiability of operator monotonic (negative complete Bernstein) functions of negative and nonpositive operators on Banach spaces is investigated. The results may be regarded as a contribution to the Hirsch functional calculus.
Cite
@article{arxiv.1806.05066,
title = {Perturbation determinants on Banach spaces and operator differentiability for Hirsch functional calculus},
author = {Adolf Mirotin},
journal= {arXiv preprint arXiv:1806.05066},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1805.01337