Best approximation by diagonal compact operators
Functional Analysis
2013-03-05 v1 Operator Algebras
Abstract
We study the existence and characterization properties of compact Hermitian operators C on a separable Hilbert space H such that ||C|| is less or equal than || C + D ||, for all D in D(K(H)). This property is equivalent to || C || = min{||C+D||: D in D(K(H))} = dist (C,D(K(H))), where D(K(H)) denotes the space of compact diagonal operators in a fixed base of H and ||.|| is the operator norm. We also exhibit a positive trace class operator that fails to attain the minimum in a compact diagonal.
Cite
@article{arxiv.1303.0739,
title = {Best approximation by diagonal compact operators},
author = {Tamara Bottazzi and Alejandro Varela},
journal= {arXiv preprint arXiv:1303.0739},
year = {2013}
}
Comments
12 pages