Analysis Research Group

Operator Algebras, C*-algebras, and Operator Spaces




Dr. David Blecher
Ph.D., University of Edinburgh in Scotland, 1988
M.Sc., Cambridge University in England, 1985
B.Sc., University of the Witwatersrand, 1983
(Curriculum Vita)

Dr. Blecher is a professor at the University of Houston, and has been the recipient of the UH Award for Excellence in Research and Scholarship. He has also been the recipient of several NSF grants. His research interests include Operator Algebras, Operator Spaces, and Dual Algebras. He is the author of the the following books and monographs:
  • Operator algebras and their modules---an operator space approach by David Blecher and Christian Le Merdy, London Mathematical Society Monographs. New Series, 30. Oxford Science Publications. The Clarendon Press, Oxford University Press, Oxford, 2004. x+387 pp.
  • Categories of operator modules (Morita equivalence and projective modules) by David Blecher, Paul Muhly, and Vern Paulsen, Mem. Amer. Math. Soc. 143 (2000), no. 681, viii+94 pp.
  • The calculus of one-sided M-ideals and multipliers in operator spaces by David Blecher and Vrej Zarikian, Mem. Amer. Math. Soc. 179 (2006), no. 842, viii+85 pp



Dr. Vern Paulsen
Ph.D., University of Michigan, 1977
B.A., Western Michigan University, 1973
(Curriculum Vita)

Dr. Paulsen is a John and Rebecca Moores Scholar and Professor of Mathematics at the University of Houston. He serves on the editorial boards of the Houston Journal of Mathematics and Positivity. He is the recipient of a University of Houston Research Excellence Award, a College of Natural Sciences and Mathematics Teaching Excellence Award and has been continuously funded by the NSF since 1983. His research interests include operator algebras, completely bounded maps, frames, quantum computation, and function theoretic operator theory. He is the author of the following books and monographs:
  • Completely bounded maps and operator algebras by Vern Paulsen, Cambridge Studies in Advanced Mathematics 78. Cambridge University Press, Cambridge, 2002. xii+300 pp.
  • Categories of operator modules (Morita equivalence and projective modules) by David Blecher, Paul Muhly, and Vern Paulsen, Mem. Amer. Math. Soc. 143 (2000), no. 681, viii+94 pp.
  • Completely bounded maps and dilations by Vern Paulsen, Pitman Research Notes in Mathematics Series 146. Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1986. xii+187 pp.
  • Hilbert modules over function algebras by Ron Douglas and Vern Paulsen, Pitman Research Notes in Mathematics Series, 217. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. vi+130 pp.



Dr. Mark Tomforde
Ph.D., Dartmouth College, 2002
M.A., Dartmouth College, 1999
B.A., Gustavus Adolphus College, 1997
(Curriculum Vita)

Dr. Tomforde is an assistant professor at the University of Houston, and was an NSF postdoc from 2002-2005 at the University of Iowa. His research interests include C*-algebras, Discrete Dynamical Systems, Frames, Leavitt Path Algebras, and the use of algebraic techniques in Operator Algebra. Selected publications:
  • Graph Algebras: Bridging the gap between analysis and algebra (book chapter) Eds. Gonzalo Aranda Pino, Francesc Perera Domenech, and Mercedes Siles Molina, Servicio de Publicaciones de la Universidad de Malaga, Malaga, Spain, 2006.
  • Uniqueness theorems and ideal structure for Leavitt path algebras, J. Algebra 318 (2007), 270--299.
  • Adding tails to C*-correspondences (with P. Muhly), Documenta Math. 9 (2004), 79-106.
  • Topological quivers (with P. Muhly), Internat. J. Math. 16 (2005), 693--756.
  • A unified approach to Exel-Laca algebras and C*-algebras associated to graphs, J. Operator Theory 50 (2003), 345-368.
  • The C*-algebras of arbitrary graphs (with D. Drinen), Rocky Mountain J. Math. 35 (2005), 105--135.




GRADUATE STUDENTS



Upasana Kashyap
Advisor: David Blecher

Sonia Sharma
Advisor: David Blecher

Meghna Mittal
Advisor: Vern Paulsen

Sneh Lata
Advisor: Vern Paulsen

Blerina Xhabli
Advisor: Vern Paulsen

Melahat Almus
Advisor: David Blecher

Timothy Rainone
Advisor: To Be Decided

Ali Kavruk
Advisor: To Be Decided


Here is a list of former Analysis graduate students.