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Professor Mathematics dpitts2@unl.edu 213 Avery Hall

Contact Information

Mailing Address:
213 Avery Hall
Department of Mathematics
University of Nebraska-Lincoln
Lincoln, NE 68588-0130


FAX: 402-472-8466

Teaching (Spring 2021)

Math 925,Complex Analysis.
Office hours: MWF 10:00-11:00 a.m.

Research

My research interests are in Operator Theory/Operator Algebras.

Here is a complete list of my publications.

Below are some selected publications.
  • 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.
  • 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'.
  • 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
  • Close CSL Algebras are Similiar, Mathematiche Annalen, 300 (1994), 149–156. Published article at Mathematiche Annalen
  • 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
  • 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
  • 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
  • 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.
  • 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
  • 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
  • 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, 160–191. Published article at Journal of Functional Analysis
  • 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
  • Norming Algebras and Automatic Complete Boundedness of Isomorphisms of Operator Algebras, Proc. American Math. Soc, Volume 136, number 5, May 2008, 1757–1768. Published article at Proceedings of American Math Soc
  • Structure for Regular Inclusions. (Unpublished). This 2012 preprint can be downloaded from the arXiv. Notes and Updates: 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 updated and will appear in a forthcoming Journal of Functional Analysis article. A preprint version of the JFA article is Structure for Regular Inclusions. II: Cartan envelopes, pseudo-expectations and twists , and is also listed below. The results of section 7 will appear elsewhere.
  • 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
  • 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
  • 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.
  • 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.
  • 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.
  • Cartan Triples (with A. Donsig and A. Fuller), International Mathematics Research Notices. Online published version (64 pages): rnz340, https://doi.org/10.1093/imrn/rnz340
  • Characterizing Groupoid C*-Algebras of Non-Hausdorff Etale Groupoids (with R. Exel). Preprint on arXiv
  • 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.
  • 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.
  • 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..
  • Regular Ideals of Graph Algebras (with J. Brown, A. Fuller and S. Reznikoff). Preprint on arXiv.