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Professor Vern Paulsen

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TEACHING

Math 1431, Section 13203, Spring 2013
This course meets 4--5:30 MW in SEC 101.
1431 Syllabus
Department Syllabus with Homework: Homework Link
A calendar of all on-line quizes and test times: 1431 Calendar
Link to CASA and CourseWare: CASA

Some helpful tips, look at these more than once, I will update throughout the semester: 1431 Tips
Practice Test2: Practice Test2
Notes from 2/20: Notes


Math 3333, Section 17636, Spring 2013
This course meets 12--1 MWF in CBB104
3333 Syllabus
Final Exam, May 3, 11am--2pm
Grading: There will be two tests, HW part 1, HW part 2, two parts to final exam. Each of these is worth 100pts
I will keep 5 of these scores.
HW1, Due 1/25: 1.2, 1.3, 1.6, 1.8, 1.9
HW2, Due 1/30: 2.3, 2.4. Write sentences to explain.
HW3, Due 2/4: 3.4, 3.6
HW4, Due 2/8: 4.1a,g,s,t,j, 4.2a,g,s,t,j, 4.8, 4.14b
HW5, Due 2/13: 8.1, 8.2
HW6, Due 2/18: 9.1, 9.2, 9.3
HW7, Due 2/22: 9.10--all 3 parts, give proofs.
HW8, Due 2/27: 10.8, 10.9, 10.10
Test 1 is on Friday, March 8
Practice Test 1: Practice Test 1
HW9, Due 3/22: 12.2, 12.6a
HW10, Due 3/27: 14.2, 14.4 on both problems, use theorems to justify
HW11, Due 3/29: 14.5a,b, 14.6a, 14.8
The total of HW1+...+HW8 computed as a percent is the HW Part 1 grade.
HW12, Due 4/3: 15.1, 15.4
HW13, Due 4/8: 17.6, 17.9a,b, 17.10c, 17.12a,b
HW14, Due 4/12: 18.6, 18.8, 18.10
HW15, Due 4/17: 19.2, 19.3
HW16, Due 4/22: 28.7, 28.8
Practice Final Exam: Practice Final
Final Exam, May 3, 11am--2pm in CBB104
Solutions to Test 2: Solutions

RESEARCH


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 CV.pdf file


Recent Publications

Copies of some of my student's theses are available here.

Completely Bounded Maps and Operator Algebras, Cambridge University Press, February 2003. cover.jpeg
Solutions to Exercises Prepared by Mrinal Ragupathi Solutions Manual .

Complete positivity of the map from a basis to its dual basis(with F. Shultz) Arxiv Abstract

The isomorphism relation for separable C*-algebras(with G.A. Elliott, I. Farah, C. Rosendal, A.S. Toms, and A. Tornquist) Arxiv Abstract

Operator Systems from Discrete Groups(with D. Farenick, A.S. Kavruk and I. Todorov) Arxiv Abstract

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

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 Journal of Functional Analysis, 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 , Journal of Functional Analysis, 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 University University Math. J., to appear.

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. Func. 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. Func. 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 Science China Mathematics: Kadison's Proceedings, to appear.

A dynamical systems approach to the Kadison-Singer problemdynks.pdf, Journal of Functional Analysis, 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. Reprints available.

Characterizations of Essential Ideals as Operator Modules (with M. Kaneda), J.O.T., 49(2003), 245-262. Reprints available.

Diffusing with Stefan and Maxwell (with N.R. Amundson and T.-W. Pan), AIChE, April 2003, Vol.49, No. 4, 813-830. Reprints available.

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, posted on arXiv




Last updated: January 28, 2013