Welcome to Vern Paulsen's home page


Professor Vern Paulsen

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TEACHING


Winter 2017, PMath 810--Banach algebras and operator theory, T-Th, 9:30--11:00
Course Description
Homework

Fall 2016, A Survey of Functional Analysis Methods for QIT, PMath 990, or QIC 890, M-W, 10--11:30, QNC 1201
Course Description
Course Notes

Winter 2016, Entanglement and Non-Locality, PMath 990, Tu-Th 12:00-1:20, QIC 890
Course Description
Course Notes


Fall 2015, PMath 990, Matrix Analysis, MWF 2:30-3:20, M3-2134
Homework Assignments Updated: 11/27
Course Notes Updated: 11/19

RESEARCH


Research interests: Operator Algebras, Operator Theory, Frame Theory, Reproducing Kernel Hilbert Spaces, Quantum Computation and Quantum Information Theory.

Curriculum Vita, including a list of all publications CV.pdf file


Recent Publications


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

An Introduction to the Theory of Reproducing Kernel Hilbert Spaces, Cambridge Studies in Advanced Mathematics, 152, Cambridge University Press, 2016. cover
This is a collection of errata for the RKHS book:Errata

Completely Bounded Maps and Operator Algebras, Cambridge Studies in Advanced Mathematics, 78, Cambridge University Press, 2003. cover.jpeg
Solutions to Selected Exercises Prepared by Mrinal Ragupathi Solutions Manual .

Composition of PPT maps(with M. Kennedy and N. Manor) arXiv link

Complexity and capacity for quantum channels(with R. Levene and I. Todorov) arXiv link

Non-closure of the set of quantum correlations via graphs(with K. Dykema and J. Prakash) arXiv link

The Delta Game(with K. Dykema and J. Prakash) arXiv link

A synchronous game for binary constraint systems(with S.-J. Kim and C. Schafhauser) arXiv link Journal of Math. Physics, to appear

Reverse Cholesky factorization and tensor products of nest algebras(with H.J. Woerdeman) arXiv link Proc. Amer. Math. Soc., to appear

Algebras, synchronous games and chromatic numbers of graphs(with J.W. Helton, K.P. Meyer, and M. Satriano) Expanded Version

Complete spectral sets and numerical range(with K.R. Davidson and H.J. Woerdeman), Proc. Amer. Math. Soc., to appear arXiv link

Unitary correlation sets(with S.J. Harris), IEOT, to appear arXiv link

Perfect Embezzlement of Entanglement(with R. Cleve and L. Liu) J. Math. Phys., 58, 012204 (2017); http://doi.org/10.1063/1.4974818 arXiv link

Tensor Products of the Operator System Generated by the Cuntz Isometries(with D. Zheng), J. Operator Theory 76:1(2016), 67-91 doi: 10.7900/jot.2015aug04.2093 arXiv link

Quantum Graph Homomorphisms via Operator Systems(with C. Ortiz) ArXiv Abstract Linear Alg. and Appl., Vol 497, 15 May 2016, 23-43, doi: 10.1016/j.laa2016.02.019

The SOH Operator System(with W. Ng)ArXiv Abstract

Correlation Minimizing Frames in Small Dimensions(with G. Getzelman and N. Leonhard)Arxiv Abstract

Synchronous Correlation Matrices and Connes' Embedding Conjecture(with K. Dykema), Journal of Mathematical Physics, 57, 015215 http://dx.doi.org/10.1063/1.4936751 Arxiv Abstract

Extensions of the Inequalities of Hardy and Hilbert(with D. Singh)Arxiv Abstract

The Functional Analysis of Quantum Information Theory(edited by Ved Prakash Gupta, Prabha Mandayam, V. S. Sunder)Arxiv Abstract

A Spectral Characterization of AN Operators(with S. Pandey), Journal of the Australian Mathematical Society, 102(2017), no.3, 369-391 Journal Link

Lovasz theta type norms and Operator Systems(with C. Ortiz) Arxiv Abstract Linear Alg. and Appl., Vol. 477, 15 July 2015, 128-147, doi: 10.1016/j.laa.2015.03.022

Estimating Quantum Chromatic Numbers(with S. Severini, D. Stahlke, I. Todorov and A. Winter)arXiv link J. Funct. Anal. 270 (2016), no. 6, 2188?2222.

Quantum chromatic numbers via operator systems(with I. Todorov) Arxiv Abstract Q. J. Math. 66(2015), no. 2, 677-692.

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 Math. Res. Lett. 20(2013), no. 6, 1071-1080.

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, J. Operator Theory 70 (2013), no. 2, 573?590.

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, 102(1)(2011), 25-49.

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 envelope Arxiv Abstract, TAMS, Volume 363, Number 9, September 2011, 4735-4755.

An operator algebraic proof of Agler's factorization theorem(with S. Lata and M. Mittal)Arxiv 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) Arxiv Abstract IUMJ, Vol. 58, No. 2, 2009, 709--732.

Representations of logmodular algebras(with M. Raghupathi) Arxiv Abstract 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) Arxiv 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) Arxiv Abstract , Quantum Inf. Comput., 9(2009), no. 1-2, 16-35.

Vector Spaces with an Order Unit(with M. Tomforde) Arxiv Abstract , IUMJ, 58(2009), no. 3, 1319-1359.

Injectivity and projectivity in analysis and topology(with D. Hadwin) Arxiv Abstract Sci. China Math. 54 (2011), no. 11, 2347?2359.

Lectures on the Kadison-Singer Problem Lecture Notes

A dynamical systems approach to the Kadison-Singer problemArxiv Abstract, J. Funct. Anal., 255(2008), 120--132.

Some new equivalences of Anderson's paving conjectures(with M. Ragupathi)Arxiv Abstract, Proc. AMS, Vol. 136, No. 12, Dec. 2008, 4275-4282.

Stably Isomorphic Dual Operator Algebras(with G.K. Eleftherakis) Arxiv 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 Appl. Comput. Harmon. Anal. 22(2007), no. 2, 176-197.

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, Arxiv Abstract




Presentations


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