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
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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.
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A New Class of Maximal Triangular Algebras
Proceedings of the Edinburgh Mathematical Society (2018)
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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.
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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
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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.
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The Maximal Two-Sided Ideals of Nest Algebras
Journal of Operator Theory, vol. 73:2 (2015), pp. 407-416
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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.
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