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John Lindsay Orr

John Lindsay Orr

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    On the primitive ideals of nest algebras
    Proceedings of the Edinburgh Mathematical Society, vol. 63(3) (2020), pp. 737 - 760
    Preview abstract We show that Ringrose’s diagonal ideals are primitive ideals in a nest algebra (subject to the Continuum Hypothesis). This provides for the first time concerete descriptions of enough primitive ideals to obtain the Jacobson radical as their intersection. Separately, we provide a standard form for all left ideals of a nest algebra, which leads to insights into the maximal left ideals. In the case of atomic nest algebras we show how primitive ideals can be categorized by their behaviour on the diagonal, and provide concrete examples of all types. View details
    A New Class of Maximal Triangular Algebras
    Proceedings of the Edinburgh Mathematical Society (2018)
    Preview 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. View details
    Course Builder Skill Maps
    Boris Roussev
    Amit Deutsch
    Michael Lenaghan
    Mike Gainer
    Proceedings of the Third (2016) ACM Conference on Learning @ Scale (2016), pp. 89-92
    Preview abstract In this paper, we present a new set of features introduced in Course Builder that allow instructors to add skill maps to their courses. We show how skill maps can be used to provide up-to-date and actionable information on students' learning behavior and performance. View details
    The Maximal Two-Sided Ideals of Nest Algebras
    Journal of Operator Theory, vol. 73:2 (2015), pp. 407-416
    Preview abstract We give a necessary and sufficient criterion for an operator in a nest algebra to belong to a proper two-sided ideal of that algebra. Using this result, we describe the strong radical of a nest algebra, and give a general description of the maximal two-sided ideals. This also enables us to provide the final piece in the complete description of epimorphisms of one nest algebra onto another. View details
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