A New Class of Maximal Triangular Aglebras

TL;DR

This paper introduces a novel class of maximal triangular algebras with infinite multiplicity, revealing new asymptotic structures and expanding the understanding of their properties within operator algebras.

Contribution

It extends previous work by characterizing a new family of maximal triangular algebras with infinite multiplicity and analyzing their asymptotic structure.

Findings

Identified a new class of maximal triangular algebras with infinite multiplicity

Discovered unique asymptotic structural properties of these algebras

Enhanced understanding of the landscape of triangular algebras in B(H)

Abstract

Triangular algebras, and maximal triangular algebras in particular, have been objects of interest for over fifty years. Rich families of examples have been studied in the context of many w$^*$- and C$^*$-algebras, but there remains a dearth of concrete examples in B(H). In previous work, we described a family of maximal triangular algebras of finite multiplicity. Here, we investigate a related family of maximal triangular algebras with infinite multiplicity, and unearth new asymptotic structure which these algebras exhibit.