Relations and radicals in abstract lattices and in lattices of subspaces of Banach spaces and ideals of Banach algebras. Amitsur's theory revisited

TL;DR

This paper refines Amitsur's radical theory in complete lattices and applies it to the study of subspace lattices of Banach spaces and ideals in Banach and C*-algebras, advancing the understanding of their algebraic structures.

Contribution

It introduces refined methods for radicals in complete lattices and extends these to analyze subspace lattices and ideals in various Banach algebra contexts.

Findings

Enhanced understanding of radical structures in Banach space sublattices

New applications of Amitsur's theory to Banach and C*-algebra ideals

Improved classification of radicals in algebraic and topological lattice frameworks

Abstract

We refine Amitsur's theory of radicals in complete lattices and apply the obtained results to the theory of radicals in the lattices of subspaces of Banach spaces and in the lattices of ideals of Banach and C*-algebras and of Banach Lie algebras.