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Professor Vern Paulsen

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For Students of Math 3333
Text: Analysis: with an introduction to proof, 4th Edition, by Steven R. Lay, published by Pearson Prentice Hall
Syllabus: We will cover chapters 3--7
Grading: You will receive 6 grades each worth 100pts. I will keep your 5 best. Two grades will be based on HW, two on tests and two on the final exam.
Test I will cover chapters 3 and 4, Test II will cover chapters 5 and 6, the Final Exam will cover chapters 3--7.

Homework assignments:
HW1 Due 1/28: 10.4, 10.6, 10.14, 10.21, 10.22
HW2 Due 2/4: 11.3(g)--11.3(m), 11.6
HW3 Due 2/11: 12.1, 12.3, 12.4, 12.7, 12.13
HW4 Due 2/11: 16.6a, 16.6c, 16.8b, 16.8d, 16.14


For graduate students in analysis: A sample Analysis Prelim prelim041.pdf

Research interests: Operator Algebras, Operator Theory.
Curriculum Vita, including a list of all publications CV.pdf file

Recent Publications

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

Tensor Products of Operator Systems(with A. Kavruk, I. Todorov and M. Tomforde) Arxiv Abstract

Operator algebras of functions(with M. Mittal) Arxiv Abstract, J. Func. Anal., to appear.

Operator System Structures on Ordered Spaces(with I. Todorov and M. Tomforde) Arxiv Abstract, submitted.

Stable Isomorphism of Dual Operator Spaces(with G. Eleftherakis and I. Todorov) Arxiv Abstract, J. Func. Anal., to appear.

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) Abstract PAMS, to appear.

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, to appear.

Vector Spaces with an Order Unit(with M. Tomforde) Abstract , IUMJ, to appear.

Injectivity and projectivity in analysis and topology(with D. Hadwin) gequi.pdf

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 25, 2010