
27
On the Primitive Ideals of Nest Algebras
John Lindsay Orr
We show that Ringrose's diagonal ideals are primitive ideals, subject to the Continuum Hypothesis, and provide examples of a range of types of primitive ideals. Separately we provide a standard presentation for left ideals in a nest algebras, and explore their properties.
Proc. Edinburgh Math. Soc., 63 (3), 2020, 737760

26
A New Class of Maximal Triangular Algebras
John Lindsay Orr
We describe a new class of maximal tringular algebras on B(H) which have uniform infinite multiplicity nests.
Proc. Edinburgh Math. Soc., 61 (4), 2018, 909931

25
Course Builder Skill Maps
Boris Roussev, Pavel Simakov, John Orr, Amit Deutsch, John Cox, Michael Lenaghan, Mike Gainer
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 uptodate and actionable information on students' learning behavior and performance.
Proceedings of the Third (2016) ACM Conference on Learning @ Scale, 2016, 8992

24
The Maximal TwoSided Ideals of Nest Algebras
John Lindsay Orr
We give a necessary and sufficient criterion for an operator in a nest algebra to belong to a proper twosided ideal of that algebra. Using this result, we describe the strong radical of a nest algebra, and give a general description of the maximal twosided ideals.
J. Operator Theory, 73, (2), 2015, 407416

23
The Stable Ideals of a Continuous Nest Algebra, II
John Lindsay Orr
The paper presents a unified description of stable ideals of a continuous nest agebra as the kernels of limits of certain diagonal compressions. This description leads to natural formulas for the quotient norm, and criteria for when two limits give rise to the same ideal. Detailed information about sums of ideals is also obtained.
J. Operator Theory, 57 (1), 2007, 67  94

22
Randomized Interval Analysis Checks for the Equivalence of Mathematical Expressions
John Lindsay Orr, Travis Fisher, Stephen Scott
The paper presents two algorithms that use Interval Analysis to make quick and effective comparisons of mathematical expressions. The algorithms are based on random sampling and admit only onesided error, in the sense that equivalent expressions are never judged unequal.
Preprint, June 2000. Manuscript 12 pages.

21
Stable Ideals of Continuous Nest Algebras
John Lindsay Orr
The paper characterizes those closed ideals of a continuous nest algebra which are fixed by the automorphism group. This provides a framework in which to organize previously known ideals, and introduce new examples.
J. Operator Theory, 45, (2), 2001, 377412

20
eGrade Student Learning Guide
John Lindsay Orr, Bradbury Franklin
Manual on effective study skills for students using my eGrade online assessment system.
(ISBN: 0471395579), John Wiley & Sons, New York, 2000

19
Online Assessment Using the Wiley WebTests
John Lindsay Orr, William J. Lewis
Describes our development of an online homework management system at the University of Nebraska.
Focus on Calculus 16, 1999, 78

18
Online Gateway Exams in Calculus
John Lindsay Orr, William J. Lewis
A description of the online Gateway Exam system which we developed at the University of Nebraska. This was an online masterylearning system to ensure core computational competency in students in Calculus I and II.
Focus on Calculus 14, 1998, 67

17
Principal Bimodules of Nest Algebras
K. R. Davidson, John Lindsay Orr
We study weakly closed bimodules of nest algebras, and completely characterize those which are singly generated.
J. Functional Analysis, 157, 1998, 488533

16
Factorization of Triangular Operators and Ideals Through the Diagonal
John Lindsay Orr, David R. Pitts
Let D be a fixed diagonal operator. We give necessary and sufficient conditions for an upper triangular operator X to factor through X as ADB, where A and B are upper triangular operators. This leads to a description of the ideal generated by a diagonal operator in the algebra of upper triangular operators.
Proc. Edinburgh Math. Soc., 40, 1997, 227241

15
Connectedness of the Invertibles in Certain Nest Algebras
K. R. Davidson, John Lindsay Orr, D. R. Pitts
In an earlier paper (The Invertibles are Connected in Infinite Multiplicity Nest Algebras) it was shown that the group of inveribles in a nest algebra is connected, provided the algebra has infinite multiplicity. This paper extends that result to essentially all nest algebras that do not contain a copy of the algebra of infinite upper triangular matrices. It is still unknown whether the invertible group is connected in such an algebra.
Canadian Math. Bulletin. 38, (4), 1995, 412420

14
Shuffling of Linear Orders
John Lindsay Orr
Canadian Math. Bulletin, 38, (2), 1995, 223229

13
Some Representations of TAF Algebras
John Lindsay Orr, Justin R. Peters
Pacific J. Math., 167, (1), 1995, 129161

12
The Invertibles are Connected in Infinite Multiplicity Nest Algebras
K. R. Davidson, John Lindsay Orr
This paper shows that the group of invertibles is connected in nest algebras with infinite multiplicity. (Infinite multiplicity in this context means that the nest has no finite rank atoms.)
Bull. London Math. Soc., 27, 1995, 155161

11
Triangular Algebras and Ideals of Nest Algebras
John Lindsay Orr
This work is motivated by a construction proposed by Kadison and Singer for building new maximal triangular algebras out of nest algebras and their ideals. This leads to the study of diagonaldisjoint ideals of nest algebras. We show that Larson's ideal is the largest diagonaldisjoint ideal in any nest algebra. From this we can construct the first concrete examples of maximal triangular algebras in B(H) which are not nest algebras. These examples allow us to answer longstanding questions on the structure of maximal triangular algebras. We also introduce and classify new families of maximal triangular algebras.
Memoirs of the Amer. Math. Soc., 562 (117), 1995.

10
Epimorphisms of Nest Algebras
K. R. Davidson, K. Harrison, John Lindsay Orr
We attempt a classification of the epimorphisms that can map between two nest algebras. In nearly all cases this classification is achieved. In all cases the epimorphisms are automatically continuous.
International J. Math., 6, (5), 1995, 657687

9
The Jacobson Radical of a CSL Algebra
K. R. Davidson, John Lindsay Orr
We develop a general framework to characterize the Jacobson radical of a completely distributive CSL algebra, which reduces the problem to a combinatoric problem. We solve this combinatoric problem in two dimensions, hence characterizing the Jacobson radical of widthtwo CSLs (both the completely distributive case, and the non CD ).
Transactions of the Amer. Math. Soc., 334, (2), 1994, 925947

8
The Maximal Ideals of a Nest Algebra
John Lindsay Orr
This paper gives a concrete description of the maximal ideals of a continuous nest algebra. The concrete form enables us to describe all ideals in the lattice of ideals generated by the maximal ideals. It is shown that this lattice contains all closed ideals which contain the ideal which is the meet of the maximal ideals. This lattice is shown to be closed under sums and products, which coincide with joins and meets of ideals.
J. Functional Analysis, 124, (1), 1994, 119134

7
An Estimate on the Norm of the Product of Infinite Block Operator Matrices
John Lindsay Orr
Using methods of infinite Ramsey theory, a lower bound is found for the quantity sup( XDY ) where X and Y are infinite block operator matrices and the supremum is taken as D ranges over all contractive block diagonal operators.
J. Combinatorial Theory (Series A), 63, (2), 1993, 195209

6
Representation and Refinement for Reflexive Operator Algebras with Completely Distributive Commutative Subspace Lattice
John Lindsay Orr, S. C. Power
Indiana U. Math. J., 40, (2), 1991, 617638

5
On the closure of triangular algebras
John Lindsay Orr
An example is presented of a maximal triangular subalgebra of B(H) which is not normclosed. Variants of this example show that transitive maximal triangular subalgebras of B(H) and maximal triangular subalgebras of the II_{1 }factor can also fail to be normclosed.
Amer. J. Math., 112, 1990, 481497

4
Triangular algebras and ideals of nest algebras
John Lindsay Orr
This announcement reports on the results of Triangular Algebras and Ideals of Nest Algebras and The Maximal Ideals of a Nest Algebra
Bull. Amer. Math. Soc., 23, (2), 1990, 461467

3
On generators of the radical of a nest algebra
John Lindsay Orr
Ths paper characterizes those nest algebras for which the Jacobson radical is singly generated. It is shown that the radical is singly generated if and only if it is countably generated.
J. London Math. Soc., 40, (2), 1989, 547562

2
A note on quasicentral approximate units in B(H)
John Lindsay Orr
Proc. Amer. Math. Soc., 105, (1), 1989, 149150

1
Diagonaldisjoint ideals of nest algebras
John Lindsay Orr
Ph.D. Thesis, University of London, 1989