Joint numerical ranges and compressions of powers of operators
Functional Analysis
2018-08-15 v2
Abstract
We identify subsets of the joint numerical range of an operator tuple in terms of its joint spectrum. This result helps us to transfer weak convergence of operator orbits into certain approximation and interpolation properties for powers in the uniform operator topology. This is a far-reaching generalization of one of the main results in our recent paper posted as arXiv:1607.00040. Moreover, it yields an essential (but partial) generalization of Bourin's "pinching" theorem. It also allows us to revisit several basic results on joint numerical ranges, provide them with new proofs and find a number of new results.
Keywords
Cite
@article{arxiv.1711.07931,
title = {Joint numerical ranges and compressions of powers of operators},
author = {Vladimir Muller and Yuri Tomilov},
journal= {arXiv preprint arXiv:1711.07931},
year = {2018}
}
Comments
30 pages, This is a version of the paper to appear in Journal of the London Mathematical Society