M. O’Brien

collaborators

2 papers

math.FA2021

Net convergence structures with applications to vector lattices

M. O'Brien, V. G. Troitsky, J. H. van der Walt

Convergence is a fundamental topic in analysis that is most commonly modelled using topology. However, there are many natural convergences that are not given by any topology; e.g.,…

math.FA2016

Unbounded Norm Convergence in Banach Lattices

Y. Deng, M. O'Brien, V. G. Troitsky

A net $(x_{α})$ in a vector lattice $X$ is unbounded order convergent to $x \in X$ if $∣ x_{α} - x ∣ \land u$ converges to $0$ in order for all $u \in X_{+}$ . This convergence ha…