Absolutely minimum attaining closed operators
Functional Analysis
2019-04-10 v4 Operator Algebras
Spectral Theory
Abstract
We define and discuss properties of the class of unbounded operators which attain minimum modulus. We establish a relationship between this class and the class of norm attaining bounded operators and compare the properties of both. Also we define absolutely minimum attaining operators (possibly unbounded) and characterize injective absolutely minimum attaining operators as those with compact generalized inverse. We give several consequences, one of them is that every such operator has a non trivial hyperinvariant subspace.
Cite
@article{arxiv.1606.05736,
title = {Absolutely minimum attaining closed operators},
author = {S. H. Kulkarni and G. Ramesh},
journal= {arXiv preprint arXiv:1606.05736},
year = {2019}
}
Comments
Submitted for publication. The article is rewritten. Many proofs are simplified