Approximate identities for Ideals in $L(L^p))$
Functional Analysis
2024-02-22 v1
Abstract
The main result is that the only non trivial closed ideal in the Banach algebra of bounded linear operators on , , that has a left approximate identity is the ideal of compact operators. The algebra has at least one non trivial closed ideal that has a contractive right approximate identity as well as many, including the unique maximal ideal, that do not have a right approximate identity.
Cite
@article{arxiv.2402.13438,
title = {Approximate identities for Ideals in $L(L^p))$},
author = {William B. Johnson and Gideon Schechtman},
journal= {arXiv preprint arXiv:2402.13438},
year = {2024}
}