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Professor Vern Paulsen

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For Students of Math 4332, Section 13669 and Math 6313, Section 16202, Spring 2012
This course meets 11-12, MWF in 347 PGH.
Mathematics 4331 or its equivalent is required for this course.
Recommended Texts: Maxwell Rosenlicht, "Introduction to Analysis", Dover books
Georgi E. Shilov, "Elementary Real and Complex Analysis", Dover books
Topics to be covered include:
Sequences and series of functions(S Chapter 6), including power series and Fourier series, Approximation of functions, Theorems of Multivariable Calculus, including inverse and implicit function theorems.
Since we are not following any book exactly, course notes are available here: 4332 Notes
Solutions to HW problems are here: 4332 Solutions
We will assume that you are familiar with the material from the first half of this course. Math 4331 notes are here: 4331 Notes
Grading: HW will be 2x100pts, Midterm 2x100pts, Final Exam 2X100pts. Of these 6 grades I will keep your best 500pts.
The Final Exam is Wednesday, May 9, 11--2 in our classroom
For Students of Math 6395, Section 23301, Fall 2011
This course will cover the mathematics needed to understand the theory of quantum computing, together with an introduction to some of the topics of interest to researchers in this area(quantum algorithms, quantum error correction, entanglement).
For Students of Math 1451, Spring 2011
Grading: There will be 3 in class tests and HW each worth 100pts, no final exam. A test on the day of the final can be used to substitute one test.
Homework Assignments:
HW1, Due 1/24(Changed to 2/2), Section 12.1, problems 3, 6a, 7, 8, 9, 10, 11, 16, 20, 32
HW2, Due 1/26, Section 12.2, problems 14, 18, 22, 26, 31
HW3, Due 1/31, Section 12.3, problems 2--20 even, 36,38,46,48
HW4, , Section 12.4, problems 2,4,6,10,30,40
HW5, Due 2/9, Section 12.5, problems 2,4,16,22,26,34
HW6, Due 2/16, Section 13.1, problems 8,10,28, Section 13.2, problems 4,6,10,18,40
HW7, Due 2/23, Section 13.3, problems 4, 24, 44
A Sample of Test I Sample Test
Test I on Thursday, March 3
HW8, Due 3/21, Section 14.1, problems 14,40; Section 14.3, problems 16,18,30,36,40,54,62
HW9, Due 3/23, Section 14.4, problems 2,6,8,19; section 14.5, problems 2,10,22,36,38
HW10, Due 3/28, Section 14.6, problems 4,6,12,22,24,28,34,40
HW11, Due 3/30, Section 14.7, problems 6,10,12,32, 34
HW12, Due 4/4, Section 15.2, problems 4,6,8,16,18,20
Test II on Thursday, April 7
Sample of Test II Sample Test II
HW13, Due 4/11, Section 15.3, problems 2,4,6,10,14,20,40,46
HW14, Due 4/13, Section 15.4, problems 6,8,20,26
HW15, Due 4/25, Section 15.8, problems 4, 22, 24
HW16, Due 4/27, Section 15.6, problems 4, 10, 14, 16: Section 15.7, problems 18, 20, 28
HW17, Due 5/2, Section 15.9, problems 2,6,12,20
Test III on Thursday, April 28
Review for Test III and Final Review
Final Exam, Tuesday, May 10, 2--5pm
Research interests: Operator Algebras, Operator Theory, Frame Theory, Reproducing Kernel Hilbert Spaces. 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 .

Operator system quotients of matrix algebras and their tensor products(with D. Farenick) Arxiv Abstract

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

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, to appear.

Syndetic Sets and Amenability Arxiv Abstract, Proceedings of the AMS, to appear.

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, to appear.

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 26, 2011