A diagonal principle for nets
Functional Analysis
2023-04-11 v1
Abstract
In our work, we provide a constructive proof of a generalized version of Cantor's diagonal argument for nets. This result expands the well-known technique beyond sequences, allowing it to be applied to a broader context. This result has significant potential applications in various fields, and we demonstrate a few of these in our work. One such application is the solution to a previously open problem posed by Kandi\'c, Marabeh, and Troitsky. Specifically, we show that the set of unbounded norm compact operators from a Banach space to a Banach lattice is closed.
Cite
@article{arxiv.2304.04189,
title = {A diagonal principle for nets},
author = {Youssef Azouzi},
journal= {arXiv preprint arXiv:2304.04189},
year = {2023}
}