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A New Class of Maximal Triangular Algebras

Part of: Linear spaces and algebras of operators

Published online by Cambridge University Press:  03 May 2018

John Lindsay Orr
John Lindsay Orr*
Affiliation:
Toll House, Traquair Road, Innerleithen EH44 6PF, [email protected]
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Abstract

Triangular algebras, and maximal triangular algebras in particular, have been objects of interest for over 50 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 $B({\cal H})$. 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 a new asymptotic structure exhibited by these algebras.

Keywords

triangular algebranest algebrainfinite multiplicity

MSC classification

Primary: 47L35: Nest algebras, CSL algebras 47L75: Other nonselfadjoint operator algebras
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 4 , November 2018 , pp. 909 - 931
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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