Publications by David R. Pitts

The list below contains my publications, mostly in chronological order. Preprints are in PDF format from Adobe. (To view the files in PDF format, you must have Adobe Acrobat Reader on your computer; it can be downloaded free of charge from the Adobe Acrobat Reader Web site.)

1. Factorization Problems for Nests: Factorization Methods and Characterizations of the Universal Factorization Property, Journal of Functional Analysis, (79) (1988), 57--90.
   Published article at Journal of Functional Analysis
2. On the $K_0$ Groups of Nest Algebras, K-Theory, (2) (1989), 737--752.
   Article via Portico Access. Note: `K-Theory' seems to have been discontinued: see the discussion in Nature 448, 846-847 (23 August 2007) or visit the Eureka page for further details on the journal `K-Theory'.
3. Compactness and Complete Distributivity for Commutative Subspace Lattices (with K. R. Davidson), Journal of the London Mathematical Society (2), Vol. 42 (1990), 147--159.
   • Abstract of article at J. London Math. Soc
   • Published article at J. London Math. Soc
4. Idempotents in Nest Algebras (with D. R. Larson), Journal of Functional Analysis, 97 (1991), 162--193.
   Published article at Journal of Functional Analysis
5. Some Questions Concerning Nest Algebras (with D. R. Larson), in ``Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory,'' (Robert S. Doran, Ed.), Contemporary Mathematics, Vol. 120, (1991), 89--96.
   Link to Volume of Contemporary Mathematics
6. A Note on the Connectedness Problem for Nest Algebras, Proceedings of the American Mathematical Society, 114(1) (1992), 181--183.
   Published article in Proceedings of the American Mathematical Society
7. Perturbations of Certain Reflexive Algebras, Pacific Journal of Mathematics, 165(1) (1994), 161--180.
   Published article at Pacific Journal of Mathematics
8. Close CSL Algebras are Similiar, Mathematiche Annalen, 300 (1994), 149--156.
   Published article at Mathematiche Annalen
9. Approximate Unitary Equivalence of Completely Distributive Commutative Subspace Lattices (with K. R. Davidson), Integral Equations and Operator Theory, Vol. 22(5) (1995), 196--211.
   Published article at Integral Equations and Operator Theory
10. Connectedness of the Invertibles in Certain Nest Algebras (with K. R. Davidson and J. L. Orr), Canadian Mathematical Bulletin, 38(4) (1995), 412--420.
    Published article in Canadian Mathematical Bulletin
11. Factorization of triangular operators and ideals through the diagonal (with J. Orr), Proceedings of the Edinburgh Mathematical Society. 40 (1997), 227--241.
    Abstract and link to published article in Proceedings of the Edinburgh Mathematical Society
12. Invariant Subspaces and Hyper-reflexivity for Free Semigroup Algebras (with K. R. Davidson), Proc. London Math. Soc., 78(2) (1999), 401--430.
    • Abstract of article at Proc. London Math. Soc
    • Published article at Proc. London Math. Soc
13. The Algebraic Structure of Non-commutative Analytic Toeplitz Algebras (with K. R. Davidson), Mathematiche Annalen, 311(2) (1998), 275--303.
    • Published article at Mathematiche Annalen
    • Erratum: Mathematiche Annalen, 2015, 361(3), 1123--1124.
14. Nevanlinna--Pick Interpolation for Non-commutative Analytic Toeplitz Algebras (with K. R. Davidson), Integral Equations and Operator Theory, Vol. 31(5) (1998), 321--337.
    Published article at Integral Equations and Operator Theory
15. The Structure of Free Semigroup Algebras, (with K. R. Davidson and E. G. Katsoulis), Journal fur die reine und angewandte Mathematik (Crelle's Journal), Vol. 533, (2001), 99--125.
    Published article at Crelle
16. Automatic Closure of Invariant Linear Manifolds for Operator Algebras, (with A. Donsig and A. Hopenwasser), Illinois Math. J., Vol 45(3), (2001), 787--802.
    Published article at Illinois Journal of Mathematics
17. Algebraic Isomorphisms and Spectra of Triangular Limit Algebras, with Allan Donsig and Stephen Power, Indiana University Math. J., Vol. 50, (2001), 1131--1147.
    • Published article at Indiana University Mathematics Journal
    • Erratum: Indiana University Math. J., Vol. 54 (2005), 1217--1218.
18. Global Existence and Non-existence Theorems for Nonlinear Wave Equations, (with M. Rammaha), Indiana University Math. J., vol. 51, (2002), 1479--1509.
    Published article at Indiana University Mathematics Journal
19. Absolutely Continuous Representations and a Kaplansky Density Theorem for Free Semigroup Algebras, (with K. Davidson and J. Li) Journal of Functional Analysis, Volume 224, Issue 1, 1 July 2005, Pages 160-191.
    Published article at Journal of Functional Analysis
20. Coordinate Systems and Bounded Isomorphisms, (with A. Donsig), Journal of Operator Theory, Vol. 59(2), (2008), 359--416.
    Published article available at Journal of Operator Theory
21. Norming Algebras and Automatic Complete Boundedness of Isomorphisms of Operator Algebras, Proc. American Math. Soc, Volume 136, number 5, May 2008, pages 1757--1768.
    Published article at Proceedings of American Math Soc
22. Structure for Regular Inclusions. (Unpublished)
    This 2012 preprint can be downloaded from the arXiv or from here.
    Notes and Updates:
    Readers should consult the updated versions of this article as follows.
    • The results of sections 1--6 and 9 in this 2012 preprint appear in the article, Structure for Regular Inclusions. I. in the Journal of Operator Theory, also listed below. In this published article, many of the proofs of sections 1--6 and 9 have been streamlined or extended, the role of Frolik's theorem is emphasized, and new results concerning minimal norms added.
    • The results of section 8 of this 2012 preprint have been expanded and updated; they appear in the Journal of Functional Analysis article, Structure for Regular Inclusions. II: Cartan envelopes, pseudo-expectations and twists (the JFA article is also listed below).
    • The results of section 7 will appear elsewhere.
23. Bimodules over Cartan MASAs in von Neumann Algebras, Norming Algebras, and Mercer's Theorem, (with J. Cameron and V. Zarikian), New York Journal of Mathematics, 19, (2013), 455-486.
    Published article in New York Journal of Mathematics
24. Isomorphisms of Lattices of Bures-Closed Bimodules over Cartan MASAs, (with A. Fuller), New York Journal of Mathematics, 19, (2013), 657-668.
    Published article in New York Journal of Mathematics
25. Von Neumann Algebras and Extensions of Inverse Semigroups (with A. Donsig and A. Fuller), Proceedings of the Edinburgh Mathematical Society, Vol. 60(1), (2016), 57-97
    Published article in Proc. Edinburgh Math. Soc.
26. Unique Pseudo-Expectations for C*-Inclusions, (with V. Zarikian), Illinois Journal of Mathematics, Vol. 59(2), Summer 2015, 449-483.
    • Published article in Illinois Journal of Mathematics
    • (You can also download the published article in the Illinois Journal of Mathematics here.)
27. Structure for Regular Inclusions. I; Journal of Operator Theory, Vol. 78(2), (2017), 357-416, doi: 10.7900/jot.2016sep15.2128.
    Published article in Journal of Operator Theory
    In addition to new results on minimal norms, this 2017 publication contains the results of sections 1-6 and 9 of the 2012 preprint ``Structure for Regular Inclusions'' listed above.
28. Cartan Triples (with A. Donsig and A. Fuller), International Mathematics Research Notices, Vol 2021 (issue 11), June 2021, 8007-8070.
    • Online version (64 pages, appeared in 2019): rnz340, https://doi.org/10.1093/imrn/rnz340
29. Characterizing Groupoid C*-Algebras of Non-Hausdorff Etale Groupoids (with R. Exel), Lecture Notes in Mathematics 2306 (2022).
    • Preprint on arXiv
30. Graded C*-Algebras and Twisted Groupoid C*-Algebras (with J. Brown, A. Fuller and S. Reznikoff), New York Journal of Mathematics, 27, (2021), 205-252.
    • Published article in the New York Journal of Mathematics
31. Intermediate C*-algebras of Cartan Embeddings (with J. Brown, R. Exel, A. Fuller and S. Reznikoff), Proc. American Math. Soc., Series B, 8, (2021), 27-41.
    • Published article in Proc. American Math. Soc.
32. Structure for Regular Inclusions. II: Cartan Envelopes, Pseudo-Expectations and Twists. Journal of Functional Analysis, Volume 281, Issue 1, 1 July 2021, 108993
    This article introduces the idea of a Cartan envelope for a regular inclusion and studies the relationship between the Cartan envelope, pseudo-expectations and twists. Updated and streamlined versions of results of Section 8 of the 2012 preprint, ``Structure for Regular Inclusions,'' listed above are included in this article.
    • Published article available from J. Funct. Anal.
33. Regular Ideals of Graph Algebras (with J. Brown, A. Fuller and S. Reznikoff). Rocky Mountain J. Math., 52, (2022), No. 1, 43-48.
    • Published version at RMJM
    • Preprint on arXiv
34. Normalizers and Approximate Units for Inclusions of C*-Algebras. Indiana University Mathematics Journal, to appear.
    • Preprint at Indiana University Mathematics Journal
    • Preprint on arXiv
35. Exotic Ideals in Represented Free Transformation Groups (with R. Exel and V. Zarikian), Bulletin of the London Mathematical Society
    • Online published version at Bulletin London Math. Soc.
    • Preprint on arXiv