Research Publications
John Lindsay Orr
 
20. The Stable Ideals of a Continuous Nest Algebra, II
Preprint, February 2005. Manuscript 25 pages. [math.OA/0502455]

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.


19. Randomized Interval Analysis Checks for the Equivalence of Mathematical Expressions
Preprint, June 2000. Manuscript 12 pages.

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 one-sided error, in the sense that equivalent expressions are never judged unequal.


18. Stable Ideals of Continuous Nest Algebras.
J. Operator Theory, 45, (2), 2001, 377-412

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.


17. Principal Bimodules of Nest Algebras
J. Functional Analysis, 57, 1998, 488-533

(with K. R. Davidson)

We study weakly closed bimodules of nest algebras, and completely characterize those which are singly generated.


16. Factorization of Triangular Operators and Ideals Through the Diagonal
Proc. Edinburgh Math. Soc., 40, 1997, 227-241

(with D. 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.


15. Connectedness of the Invertibles in Certain Nest Algebras
Canadian Math. Bulletin. 38, (4), 1995, 412-420

(with K. R. Davidson and 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.


14. Shuffling of Linear Orders.
Canadian Math. Bulletin, 38, (2), 1995, 223-229
 
 


13. Some Representations of TAF Algebras
Pacific J. Math., 167, (1), 1995, 129-161

(with J. R. Peters).


12. The Invertibles are Connected in Infinite Multiplicity Nest Algebras
Bull. London Math. Soc., 27, 1995, 155-161

(with K. R. Davidson)

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.)


11. Triangular Algebras and Ideals of Nest Algebras
Memoirs of the Amer. Math. Soc., 562 (117), 1995.

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 diagonal-disjoint ideals of nest algebras. We show that Larson's ideal is the largest diagonal-disjoint 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.


10. Epimorphisms of Nest Algebras
International J. Math., 6, (5), 1995,  657-687

(with K. R. Davidson and K. Harrison)

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.


9. The Jacobson Radical of a CSL Algebra
Transactions of the Amer. Math. Soc., 334, (2), 1994, 925-947

(with K. R. Davidson)

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 width-two CSLs (both the completely distributive case, and the non CD ).


8. The Maximal Ideals of a Nest Algebra
J. Functional Analysis, 124, (1), 1994, 119-134

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.


7. An Estimate on the Norm of the Product of Infinite Block Operator Matrices
J. Combinatorial Theory (Series A),  63, (2), 1993, 195-209
 
 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.

6. Representation and Refinement for Reflexive Operator Algebras with Completely Distributive Commutative Subspace Lattice
Indiana U. Math. J., 40, (2), 1991, 617-638

(with S. C. Power)
 


5. On the closure of triangular algebras
Amer. J. Math., 112, 1990, 481-497
 
An example is presented of a maximal triangular subalgebra of B(H) which is not norm-closed. Variants of this example show that transitive maximal triangular subalgebras of  B(H)  and maximal triangular subalgebras of the II1 factor can also fail to be norm-closed.

4. Triangular algebras and ideals of nest algebras
Bull. Amer. Math. Soc., 23, (2), 1990, 461-467
 
 This announcement reports on the results of Triangular Algebras and Ideals of Nest Algebras and The Maximal Ideals of a Nest Algebra 

3. On generators of the radical of a nest algebra
J. London Math. Soc., 40, (2), 1989, 547-562
 
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.

2. A note on quasicentral approximate units in B(H)
Proc. Amer. Math. Soc., 105, (1), 1989, 149-150


1. Diagonal-disjoint ideals of nest algebras
Ph.D. Thesis, University of London, 1989