Welcome to Vern Paulsen's home page
Professor Vern Paulsen
Math 4332, Section 12937, Math 6313, Section 15156, Spring 2014
These courses meet 11--12 MWF in AH 301
Course Notes and HW assignments will be posted on this site
Sometimes I will need to refer to results from Math 4331, so here is a set of notes for that course: Math 4331 Notes
Math 4332 Notes
Solutions to HW
A picture of the space filling curve: Curve
HW1, Due 1/24: 1.8, 1.9, 1.10.
HW2, Due 1/31: 1.22, 1.23, 1.24.
HW3, Due 2/7: 1.30, 1.35, 1.36
HW4, Due 2/14: 1.39
HW5, Due 2/21: 1.50, 1.51, 1.52
HW6, Due 2/28: 1.62, 1.63, 1.64, 1.65
HW7, Due 3/7: 1.71, 1.72, 1.73, 1.74, 1.75
Midterm Exam: This will have 3 parts, HW 6, HW 7, and 3 problems that will be given on 3/3. So do careful write-ups of HW6 and HW7!
Midterm Exam Additional Problems: 3 problems
HW8, Due 3/28: 1.117
HW9, Due 4/4: 2.9, 2.10
HW10, Due 4/18: 2.30, 2.33
HW11, Due 4/25: 2.37, 2.38, 2.51
Math 3325, Section 25342, Fall 2013, Transitions to Advanced Mathematics
This course meets 4--5:30 MW in CBB 118. Note the room change!
Final Exam, in class, December 13, 5--8pm
For additional help with HW, you can visit Carlos Ortiz, T--Th 9:30--11:30 at CASA
HW1, Due 9/4: See the last page of the Course Notes for the assignment. Total: 16
HW2, Due 9/11: Section 1.1: 4 b,d,e; 6b,d,f; 9a,b; 11b
Section 1.2: 3 a,b,c,d,e; 5b,d; 6d,f,j; 7a,d; 12a,c Total: 58
HW3, Due 9/18: Section 1.2: 16b,e; Section 1.3: 1d,i,n; 2d,i,n;6b,c; 8a,c,g; 10b,e,j Total: 38
HW4, Due 9/25: Section 1.4: 5a,d; 7h,j,k; Section 1.5: 3b,c; 6e; 9a Total: 45
HW5, Due 9/30: Section 1.6: 1h, 2a,c, 3, 4c; Section 1.7: 1g, 2b, 9a, 11a,b, 13b, 16b Total: 48
HW6, Due 10/14: Section 2.1: 1b, 6b, 13; Section 2.2: 1b,d,f,h,j, 2a,b, 9d, 11b; Section 2.3: 1b,d, 8b Total: 43
HW7, Due 10/23: Section 2.4: 6b,c,e, 7a,c,d, 8b,d; Section 2.5: 2 Total: 45
HW8, Due 10/30: Section 2.6: 5,6,7,11,18,20 Give explanations for answers not just numbers. Total: 36
Test II, in class, Wednesday, November 20, covers Chapter 2, Chapter 3.1--3.4
HW9, Due 11/6: Section 3.1: 1, 4b,f, 5a,c, 6b,c; Section 3.2: 1d,g,h,k, 5a,c,f, 9a,b,c Total: 51
HW10, Due 11/11: Section 3.3: 2a,b,c, 7, 9, Section 3.4: 1b,e,g, 5, 6 Total: 30
Here is a practice test for Test 2: Practice Test II
For updates after 11/1 see Professor Tomforde's website here: Link
Math 6397, Section 21960, Fall 2013, An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
This course meets 12-1 MWF in SEC 202. Course notes will be distributed.
Research interests: Operator Algebras, Operator Theory, Frame Theory, Reproducing Kernel Hilbert Spaces, Quantum Computation and Quantum Information Theory.
I am part of the Analysis Research Group follow the link for our activities.
Curriculum Vita, including a list of all publications
Copies of some of my student's theses are available here.
Completely Bounded Maps and Operator Algebras, Cambridge University Press, February 2003.
Solutions to Exercises Prepared by Mrinal Ragupathi Solutions Manual .
Quantum chromatic numbers via operator systems(with I. Todorov) Arxiv Abstract
Characterisations of the weak expectation property(with D. Farenick, A.S. Kavruk, and I. Todorov)Arxiv Abstracts New York Journal of Mathematics, to appear.
Complete positivity of the map from a basis to its dual basis(with F. Shultz) Arxiv Abstract Journal of Mathematical Physics 54 072201 (2013); http://dx.doi.org/10.1063/1.4812329
The isomorphism relation for separable C*-algebras(with G.A. Elliott, I. Farah, C. Rosendal, A.S. Toms, and A. Tornquist) Arxiv Abstract Mathematical Research Letters, to appear.
Operator Systems from Discrete Groups(with D. Farenick, A.S. Kavruk and I. Todorov) Arxiv Abstract, Communications in Mathematical Physics, April 2014, DOI 10.1007/s00220-014-2037-6
C*-algebras with the weak expectation property and a multivariable analogue of Ando's theorem on the numerical radius(with D. Farenick and A. Kavruk) Arxiv Abstract, Journal of Operator Theory, to appear.
Operator system quotients of matrix algebras and their tensor products(with D. Farenick) Arxiv Abstract Mathematica Scandinavica, Vol. 111, 2012, 210-243.
An approximation theorem for nuclear operator systems(with K.H. Han) Arxiv Abstract J. Funct. Anal., Vol. 261, 2011, 999-1009.
Minimal and Maximal Operator Spaces and Operator Systems in Entanglement Theory(with D. Kribs, N. Johnston and R. Pereira) JKPP_Aug31.pdf , J. Funct. Anal., Vol. 260, Issue 8, 2011, 2407-2423.
Quotients, exactness and nuclearity in the operator system category(with A. Kavruk, I. Todorov and M. Tomforde) Arxiv Abstract Advances in Math., Vol. 235, 1 March 2013, 321-360.
The Feichtinger conjecture and reproducing kernel Hilbert spaces(with S. Lata) Arxiv Abstract, Indiana Univ. Math. J. 60 (2011), no. 4, 1303–1317.
Spanning and independence properties of frame partitions(with B. Bodmann, P. Casazza and D. Speegle) Arxiv Abstract, Proceedings of the AMS, Volume 140, Number 7, July 2012, 2193-2207.
Syndetic Sets and Amenability Arxiv Abstract, Proceedings of the AMS, Volume 140, Number 6, June 2012, 1997-2001.
Syndetic Sets, Paving and the Feichtinger Conjecture Arxiv Abstract, Proceedings of the AMS, Vol. 139, No. 3, March 2011, 1115-1120.
Tensor Products of Operator Systems(with A. Kavruk, I. Todorov and M. Tomforde) Arxiv Abstract, J. Funct. Anal, 261(2011), 267-299.
Operator algebras of functions(with M. Mittal) Arxiv Abstract, J. Funct. Anal., 258(2010), 3195-3225.
Operator System Structures on Ordered Spaces(with I. Todorov and M. Tomforde) Arxiv Abstract, Proc. of the LMS, to appear.
Stable Isomorphism of Dual Operator Spaces(with G. Eleftherakis and I. Todorov) Arxiv Abstract, J. Funct. Anal., 258(2010), 260-278.
Weak expectations and the injective envelopeAbstract, TAMS, Volume 363, Number 9, September 2011, 4735-4755.
An operator algebraic proof of Agler's factorization theorem(with S. Lata and M. Mittal) Abstract PAMS, Vol. 137, No. 11, Nov. 2009, 3741-3748.
A Constrained Nevanlinna-Pick Interpolation Problem(with K.R. Davidson, M. Raghupathi, and D. Singh)
Abstract IUMJ, Vol. 58, No. 2, 2009, 709--732.
Representations of logmodular algebras(with M. Raghupathi) Final version TAMS, Vol. 363, No. 5, May 2011, 267-240.
Equiangular Tight Frames from Complex Seidel Matrices Containing Cube Roots of Unity (with B. Bodmann and M. Tomforde) Abstract LAA, 430(2009), 396--417.
Computing stabilized norms for quantum operations via the theory of completely bounded maps(with N. Johnston and D. Kribs) Abstract , QIC, 9(2009), no. 1-2, 16-35.
Vector Spaces with an Order Unit(with M. Tomforde) Abstract , IUMJ, 58(2009), no. 3, 1319-1359.
Injectivity and projectivity in analysis and topology(with D. Hadwin) gequi.pdf Sci. China Math. 54 (2011), no. 11, 2347–2359.
A dynamical systems approach to the Kadison-Singer problemdynks.pdf, J. Funct. Anal., 255(2008), 120--132.
Some new equivalences of Anderson's paving conjectures(with M. Ragupathi)newpave.pdf, Proc. AMS, to appear.
Stably Isomorphic Dual Operator Algebras(with G.K. Eleftherakis) Abstract, Math. Ann., (2008)341:99--112.
Projections and the Kadison-Singer Problem(with P. Casazza, D. Edidin and D. Kalra) Abstract Matrices and Operators, to appear.
State extensions and the Kadison-Singer Problem(with C. Akemann) ARCC-ap.pdf, AIM preprint.
Injective and projective Hilbert C*-modules, and C*-algebras of compact operators(with M. Frank) Abstract
Interpolation and balls in C^k(with J. Solazzo) Abstract JOT, 60:2(2008), 379--398.
Decoherence-insensitive quantum communication by optimal C*-encoding(with B. Bodmann and D. Kribs), Abstract IEEE Transactions on Information Theory, Vol. 53, Number 12, December 2007, 4738--4749.
Smooth frame-path termination for Higher Order Sigma-Delta Quantization(with S. Abdulbaki and B. Bodmann) HOSD-JFAA.pdf JFAA, Vol. 13, Issue 3(2007), 285--307.
Frame Paths and Error Bounds for Sigma-Delta Quantization(with B. Bodmann) sigmadelta.pdf ACHA, to appear.
Equivariant Maps and Bimodule Projections solelprob.pdf JFA 240(2006), 495-507.
An Introduction to the Theory of Reproducing Kernel Hilbert Spaces, Course Notes rkhs.pdf
Loss-Insensitive Vector Encoding with Two-Uniform Frames(with B. Bodmann) FGE_SPIE.pdf, in Wavelets XI, Proceedings of the SPIE, vol. 5914(2005), M. Papadakis, A.F. Laine, M.A. Unser (Eds.), pp. 591403-1-12.
A Simple Proof of Bohr's Inequality(with D. Singh) bohrconf.pdf
An Introduction to the Theory of Topological Groups and Their Representations, Course Notes grouprepn.pdf
Modules Over Subalgebras of the Disk Algebra(with D. Singh) diskalg.pdf IUMJ, Vol. 55, No. 5(2006), 1751-1766.
Schur multipliers and operator-valued Foguel-Hankel operators(with C. Badea), Abstract,, IUMJ, Vol. 50, No. 4(2001), 1509--1522.
Frames, Graphs and Erasures(with B. Bodmann), Abstract, LAA 404(2005), 118-146.
Extensions of Bohr's Inequality(with D. Singh) bohrext.dvi file Bull. LMS 38(2006), 991-999.
Two Reformulations of Kadison's Similarity Problem(with D. Hadwin) kadsim.dvi file JOT, Vol. 55, No. 1, Winter 2006, 3-16.
Quasimultipliers of Operator Spaces(with M. Kaneda), quasi.dvi file JFA, 217(2004), 347-365. Reprints available.
Injective Envelopes of C*-algebras as Operator Modules (with M. Frank), Pac.J. Math., 212(2003), 57-69.
Characterizations of Essential Ideals as Operator Modules (with M. Kaneda), J.O.T., 49(2003), 245-262.
Diffusing with Stefan and Maxwell (with N.R. Amundson and T.-W. Pan), AIChE, April 2003, Vol.49, No. 4, 813-830.
Optimal Frames for Erasures (with R.B. Holmes), Lin. Alg. Appl., 377(2004), 31-51.
Reprints available. opframe.pdf
Bohr's Inequality for Uniform Algebras (with D. Singh) PAMS, 132(2004), 3577-3579. Reprints available.
Lie ideals in Operator Algebras(with A. Hopenwasser), J.O.T.,52(2004), 325-340, reprints available, posted on arXiv
On the Ranges of Bimodule Projections(with A. Katavolos), Can. Bull. Math., 48(1), 2005, 97-111, reprints available, Arxiv Abstract
Operator Systems: Quotients, Duals and Tensors with Applications to Connes' Embedding Problem Banff International Research Station, February 27, 2012 Video
The Functional Analysis of Quantum Information Theory, I, Chennai, India, January 2, 2011, Youtube
The Functional Analysis of Quantum Information Theory, II, Chennai, India, January 3, 2011, Youtube
The Functional Analysis of Quantum Information Theory, III, Chennai, India, January 4, 2011, Youtube
The Functional Analysis of Quantum Information Theory, IV, Chennai, India, January 5, 2011, Youtube
The Functional Analysis of Quantum Information Theory, V, Chennai, India, January 6, 2011, Youtube
Last updated: August 14, 2013