Counterexamples to the extendibility of positive unital norm-one maps (with G. Chiribella, V. Paulsen and M. Rahaman).

Positive maps and entanglement in real Hilbert spaces (with G. Chiribella, V. Paulsen and M. Rahaman).

Interpolation and duality in algebras of multipliers on the ball (with Michael Hartz), to appear J. European Math. Soc.

Strongly Peaking Representations and Compressions of Operator Systems (with Benjamin Passer), IMRN (2022) 5037--5070.

Noncommutative Choquet theory (with Matthew Kennedy), Oct. 2022 version.

Nevanlinna-Pick Families and Singular Rational Varieties} (with Eli Shamovich), Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology, Operator Theory: Advances and Applications **278**, R. Curto et al. (eds.), Birkhauser 2020, pp.129--145.

Structure of free semigroupoid algebras (with Adam Dor-On and Boyu Li), J. Funct. Anal. **277** (2019), 3283-3350.

A proof of Boca's Theorem (with Evgenios Kakariadis), Proc. A Royal Soc. Edinburgh **149** (2019), 869-876.

Complete spectral sets and numerical range (with Vern Paulsen and Hugo Woerdeman), Proc. Amer. Math. Soc. **146** (2018), 1189-1195.
. 3, 1509–1527.

Choquet order and hyperrigidity for function systems (with Matthew Kennedy), Advances Math. **385** (2021), paper 107774 (30 pages).

Dilations, inclusions of matrix convex sets, and completely positive maps (with Adam Dor-On, Orr Shalit and Baruch Solel), IMRN **2017** (2017), 4069-4130.

Absolute continuity for commuting row contractions (with Raphael Clouatre), J. Funct. Anal. **271** (2016), 620-641.

Ideals in a multiplier algebra on the ball (with Raphael Clouatre), Trans. Amer. Math. Soc., **370** (2018), no. 3, 1509–1527.

Duality, convexity and peak interpolation in the Drury-Arveson space (with Raphael Clouatre), Adv. Math. **295** (2016), 90-149.

The unit ball of the predual of $H^\infty(\bB_d)$ has no extreme points (with Raphael Clouatre), Proc. Amer. Math. Soc. **144** (2016), 1575-1580.

Erratum to: The algebraic structure of non- commutative analytic Toeplitz algebras (with David Pitts), Math. Annalen **361** (2015), 1123--1124.

Semicrossed Products of Operator Algebras by Semigroups (with Adam Fuller and Evgenios Kakariadis)
revised March, 2015, Memoirs Amer. Math. Soc. **247** No.1168 (2017).

Semicrossed Products of Operator Algebras: A Survey (with Adam Fuller and Evgenios Kakariadis),
New York J. Math. **24Ai** (2018), 56–86.

Multipliers of embedded discs
(with Michael Hartz and Orr Shalit), Complex Analysis and Operator Theory **9** (2015), 287--321. Erratum, ibid. 323--327.

The Choquet boundary of an operator system (with Matthew Kennedy), Duke J. Math. **164** (2015), 2989-3004.

The mathematical legacy of William Arveson,
J. Operator Theory **68** (2012), 307-334.

Conjugate dynamical systems on C*-algebras (with Evgenios Kakariadis),
Int. Math. Res. Not. IMRN. **2014** (2014), 1289-1311.

A 3x3 dilation counterexample (with Man Duen Choi),
Bull. London Math. Soc. **45** (2013), 511-519.

Operator algebras for analytic varieties
(with Christopher Ramsey and Orr Shalit),
Trans. Amer. Math. Soc. **367** (2015), 1121--1150.

Dilation theory, commutant lifting and semicrossed products
(with Elias Katsoulis),
Documenta Math. **16** (2011) 781-868.

Semicrossed products of the disc algebra
(with Elias Katsoulis),
Proc. Amer. Math. Soc. **140** (2012) 3479-3484.

The isomorphism problem for some universal operator algebras
(with Christopher Ramsey and Orr Shalit),
Advances in Math. **228** (2011), 167-218.

Nevanlinna-Pick Interpolation and Factorization of Linear Functionals
(with Ryan Hamilton),
Integral Equations and Operator Theory **70** (2011), 125-149.

Isomorphisms of tensor algebras of topological graphs
(with Jean Roydor),
Indiana Univ. Math. J. **60** (2011), 1249-1266.

Commutant lifting for commuting row contractions
(with Trieu Le),
Bull. London Math. Soc. **42** (2010), 506-516.

Essentially normal operators ,
a survey article in:
*A glimpse of Hilbert space operators: Paul R. Halmos in memoriam,*
S. Axler, P. Rosenthal and D. Sarason, eds., pp. 209-222,
Oper. Theory Adv. Appl. **207**, Birkhäuser Verlag, Basel, 2010.

Dilating covariant representations of the non-commutative disc algebras
(with Elias Katsoulis),
J. Funct. Anal. **259** (2010) 817-831.

Biholomorphisms of the unit ball of $\bC^n$ and semicrossed products
(with Elias Katsoulis), in
*Operator Theory Live: conference proceedings, Timisoara, July 3-8, 2008*, 69-80,
Theta Foundation, 2010.

Nonself-adjoint operator algebras for dynamical systems
(with Elias Katsoulis), Contemporary Math. **503** (2009), 39-51.

C*-envelopes of tensor algebras for multivariable dynamics
(with Jean Roydor), Proc. Edinburgh Math. Soc. **53** (2010), 333-351.

Operator algebras with unique preduals
(with Alex Wright), Canad. Math. Bull. **54** (2011), 411-421.

Representations of higher rank graphs
(with Dilian Yang), New York J. Math. **15** (2009), 169-198.

Topological stable rank of nest algebras
(with You Qing Ji), Proc. London Math. Soc. **98** (2009), 652-678.

Semicrossed Products of Simple C*-algebras
(with Elias Katsoulis), Math. Annalen **342** (2008), 515-525.

A Constrained Nevanlinna-Pick Interpolation Problem
(with V. Paulsen, M. Raghupathi and D. Singh), Indiana J. Math. **58** (2009), 709-732.

On the topological stable rank of non-selfadjoint operator algebras
(with L. Marcoux, R. Levene and H. Radjavi), Math. Annalen **341** (2008), 239-253.

Dilation Theory for rank 2 graph algebras (with S.C. Power and Dilian Yang),
J. Operator Theory **63** (2010), 245-270.

Atomic Representations of Rank 2 Graph Algebras (with S.C. Power and Dilian Yang),
J. Funct. Anal. **255** (2008), 819-853.

Periodicity in Rank 2 Graph Algebras (with Dilian Yang),
Canad. J. Math. **61** (2009), 1239-1261.

Operator algebras for multivariable dynamics (with Elias Katsoulis),
Memoirs Amer. Math. Soc. **209** (2011), no. 982.

Transitive Spaces of Operators (with L. Marcoux and H. Radjavi)
Integral Equations & Operator Theory **61** (2008), 187-210.

A note on absolute continuity in free semigroup algebras (with Dilian Yang),
Houston J. Math. **34** (2008), 283-288.

Absolutely Continuous Representations and a Kaplansky Theorem for
Free Semigroup Algebras (with Jiankui Li and David Pitts),
J. Func. Anal. **224** (2005), 160-191.

*B(H)* is a free semigroup algebra,
Proc. Amer. Math. Soc. **134** (2006), 1753-1757.

The structure of free semigroup algebras
(with Elias Katsoulis and David Pitts),
J. reine angew. Math. (Crelle) **533** (2001), 99-125.

Isometric Dilations of non-commuting finite rank n-tuples
(with David Kribs and Miron Shpigel),
Canad. J. Math. **53** (2001), 506-545.

Nevanlinna-Pick Interpolation for non-commutative analytic
Toeplitz algebras (with David Pitts),
Integral Equations and Operator Theory **31** (1998), 321-337.

The Algebraic Structure of Non-commutative Analytic Toeplitz Algebras
(with David Pitts),
Math. Annalen **311** (1998), 275-303.

Invariant Subspaces and Hyper-reflexivity for Free Semigroup Algebras
(with David Pitts),
Proc. London Math. Soc. (3) **78** (1999), 401-430.

Free Semigroup Algebras : a survey,
*Systems, approximation, singular integral operators, and related topics*
(Bordeaux, 2000), 209-240, Oper. Theory Adv. Appl. **129**,
Birkhauser, Basel, 2001.

Isomorphisms between Topological Conjugacy Algebras (with Elias Katsoulis),
J. reine angew. Math. (Crelle) **621** (2008), 29-51.

Norms of Schur Multipliers (with Allan Donsig).
Illinois J.Math. **51** (2007), 785-807.

1-Hyperreflexivity and Complete Hyperreflexivity (with Rupert Levene).
J. Func. Anal. **235** (2006), 666-701.

Nest representations of directed graph algebras (with Elias Katsoulis).
Proc. London Math. Soc. **92** (2006), 762-790.

Tridiagonal Forms in Low Dimensions (with D.Z. Djokovic).
Lin. Alg. Appl. **407** (2005), 169-188.

Generalized Berezin Transform and Commutator Ideals
(with Ronald Douglas). Pacific J. Math. **222** (2005), 29-56.

Linear spans of unitary and similarity orbits of a Hilbert space operator
(with Laurent Marcoux).
J. Operator Theory **52** (2004), 113-132.

Meet irreducible ideals and representations of limit algebras
(with E. Katsoulis and J. Peters).
J. Func. Anal. **200** (2003),23-30.

Primitive Limit Algebras and C*-Envelopes
(with Elias Katsoulis).
Advances Math. **170** (2002), 181-205.

A Note on the Similarity Theorem for Nest Algebras.

Nests were classified up to similarity simply in terms of order type and dimension. However the original proof (also exposited in my book) appears to rely on first classifying the compact perturbations of the nest algebras. This in turn required reliance on some difficult results on derivations of C*-algebras and in particular on the theorem of Johnson and Parrott. However a careful examination of the proofs shows that this circuitous route can be avoided. This note is a study guide to allow the reader to wend his or her way through those necessary parts of the proof and avoid the unneeded results on quasitriangular operators if they choose.

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