arXiv subjects

Ayse Guven

Publications and source records attributed to Ayse Guven.

2 recordsLinked to original sources

arXiv2020

Quantitative spectral perturbation theory for compact operators on a Hilbert space

We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging to a particular compactness class. As a consequence we obtain explicitly computable upper bounds for the Hausdorff distance of the spectra of two operators belonging to the same compactness class in terms of the distance of the two operators in operator norm.

math.SP↗

arXiv2015

Explicit upper bounds for the spectral distance of two trace class operators

Given two trace class operators A and B on a separable Hilbert space we provide an upper bound for the Hausdorff distance of their spectra involving only the distance of A and B in operator norm and the singular values of A and B. By specifying particular asymptotics of the singular values our bound reproduces or improves existing bounds for the spectral distance. The proof is based on lower and upper bounds for determinants of trace class operators of independent interest.

math.SP↗