Publications

Link to my page on scholar

Books

A First Course in Functional Analysis”, CRC Press, 2017. Publisher’s website. Here is a link to a list of corrections.

“A Second Course in Functional Analysis”, CRC Press, forthcoming.

Papers

Dilation distance and the stability of ergodic commutation relations, with Malte Gerhold, preprint.

On the classification of function algebras on subvarieties of noncommutative operator balls, with Jeet Sampat, preprint.

Tensor algebras of subproduct systems and noncommutative function theory, with Michael Hartz, Canadian Journal of Mathematics, available here.

CP-Semigroups and Dilations, Subproduct Systems and Superproduct Systems: the Multi-Parameter Case and Beyond, with Michael Skeide, Dissertationes Mathematicae, Vol 585 (2023), 1-233. Available here.

Bounded perturbations of the Heisenberg commutation relation via dilation theory, with Malte Gerhold, Proceedings of the American Mathematical Society, Vol. 151 (2023), 3949-3957. Available here.

von Neumann’s inequality for row contractive matrix tuples, with Michael Hartz and Stefan Richter,  Mathematische Zeitschrift, Vol. 301 (2022), 3877-3894. Available here.

Distance between reproducing kernel Hilbert spaces and geometry of finite sets in the unit ball, with Danny Ofek and Satish Pandey, Journal of Mathematical Analysis and Applications, Vol. 500 Issue 2 (2021), 125140. Available here.

Dilations of unitary tuples, with Malte Gerhold, Satish Pandey and Baruch Solel, Journal of the London Mathematical Society, Vol. 104 No. 2 (2021), 2053-2081. Available here.

On the matrix range of random matrices, with Malte Gerhold, Journal of Operator Theory, Vol. 85 No. 2 (2021). Available here.

Dilations of q-commuting unitaries, with Malte Gerhold, International Mathematics Research Notices (2020). Available here.

Algebras of noncommutative functions on subvarieties of the noncommutative ball: the bounded and completely bounded isomorphism problem, with Guy Salomon and Eli Shamovich, Journal of Functional Analysis, Vol. 278 Issue 7 (2020), 108427. Available here.

Compressions of compact tuples, with Benjamin Passer, Linear Algebra and its Applications, Vol. 564 No. 1 (2019), 264-283. Available here.

On operator algebras associated with monomial ideals in noncommuting variables, with Evgenios Kakariadis, Journal of Mathematical Analysis and Applications, Vol. 472, (2019) Issue 1, 738-813. Available here.

Algebras of bounded noncommutative analytic functions on subvarieties of the noncommutative unit ball, with Guy Salomon and Eli Shamovich, Transactions of the American Mathematical Society, Vol. 370 No. 12 (2018), 8639–8690. Available here.

Minimal and maximal matrix convex sets, with Benjamin Passer and Baruch Solel, Journal of Functional Analysis, Vol. 274 No.11 (2018), 3197-3253. Available here.

Dilations, inclusions of matrix convex sets, and completely positive maps, with Kenneth R. Davidson, Adam Dor-On and Baruch Solel,  International Mathematics Research NoticesVol. 2017 Issue 13 (2017),  4069-4130. Available hereNote: the published version in IMRN contains an error in Section 6: an important condition (nonsingularity) is missing from the assumptions, making some of the results there incorrect as stated. This is fixed in the current arxiv version. Other sections in the paper (and hence the main results in them) are not affected. 

Spaces of Dirichlet series with the complete Pick property, with John E. McCarthy, Israel Journal of Mathematics, Vol. 220 (2017), 509–530. Available here.

Stable division and essential normality: the non-homogeneous and quasi homogeneous cases, with Shibananda Biswas, Indiana University Mathematics Journal, Vol. 67 No. 1 (2018), 169-185. . Available here.

Essential normality, essential norms and hyperrigidity, with Matthew Kennedy, Journal of Functional Analysis, Vol. 268 (2015) No. 10, 2990-3016. Available here. Here is the  Corrigendum.

Operator algebras for analytic varieties, with Kenneth R. Davidson and Christopher Ramsey, Transactions of the American Mathematical Society, Vol. 367, No. 2 (2015), 1121-1150. Available here.

Multipliers of embedded disks, with Kenneth R. Davidson and Michael Hartz, Complex Analysis and Operator Theory, Vol. 9 (2015), 287-321. Available here. Here is the Erratum.

Spectral sets and distinguished varieties in the symmetrized bidisc, with Sourav Pal, Journal of Functional Analysis, Vol. 266 No. 9 (2014), 5779-5800. Available here.

On the isomorphism question for complete Pick multiplier algebras, with Matt Kerr and John E. McCarthy, Integral Equations and Operator Theory, Volume 76 Issue 1 (2013), 39-53. Available here.

Unitary N-dilations for tuples of commuting matrices, with John E. McCarthy, Proceedings of the American Mathematical Society, Vol. 141 (2013), 563-571. Available here.

Essential normality and the decomposability of algebraic varieties, with Matthew Kennedy, New York Journal of Mathematics, Vol. 18 (2012) 877-890.

The isomorphism problem for some universal operator algebras, with Kenneth R. Davidson and Christopher Ramsey,  Advances in MathematicsVol. 228 (2011) 167-218. Available here.

Stable polynomial division and essential normality of graded Hilbert modulesJournal of the London Mathematical Society, Vol. 83 Issue 2 (2011) 273-289. Available here.

Essential normality, essential norms and hyperrigidity, with Matthew Kennedy, Journal of Functional Analysis, Vol. 268 (2015) No. 10, , 2990-3016. Available here. Here is the  Corrigendum.

Three remarks on a question of AczelAequationes Mathematicae, Vol. 84, No. 3, (2012) 201-205. Available here.

Three commuting, unital, completely positive maps that have no minimal dilation, with Michael Skeide,  Integral Equations and Operator Theory, Vol. 71 Issue 1 (2011),  55-63. Available here.

The isomorphism problem for some universal operator algebras, with Kenneth R. Davidson and Christopher Ramsey,  Advances in MathematicsVol. 228 (2011) 167-218. Available here.

Representing a product system representation as a contractive semigroup and applications to regular isometric dilations Canadian Mathematical Bulletin, Vol. 53, No. 3 (2010) 550-563.  Available here.

Subproduct systems , with Baruch Solel, Documenta Mathematica, 14 (2009), 801-868.

E-dilation of strongly commuting CP-semigroups (the nonunital case) Houston Journal of Mathematics Vol. 35 No. 1 (2011) 203-232. Available here.

Continuity of CP-semigroups in the point-strong topology , with Daniel Markiewicz, Journal of Operator Theory , Vol. 64 No. 1 (2010) 149-154. Available here.

Subproduct systems , with Baruch Solel, Documenta Mathematica, 14 (2009), 801-868.

Continuous extension of a densely parameterized semigroup , with Eliahu Levy, Semigroup Forum, Vol. 78, No. 2 (2009) 276-284. Available here.

Conjugacy of P-configurations and nonlinear solutions to a certain conditional Cauchy equation Banach Journal of Mathematical Analysis, Vol. 3, No. 1 (2009) 28-35. Available here.

What type of dynamics arise in E_0-dilations of commuting quantum Markov processes? Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 11, No. 3 (2008) 393-403. Available on the publisher’s webpage.

E_0-dilation of strongly commuting CP_0-semigroups Journal of Functional Analysis , Vol. 255, No. 1 (2008) 46-89. Available here. This paper contains a mistake. Here is the Corrigendum (available also here in JFA).

On the overdeterminedness of a class of functional equationsAequationes Mathematicae, Vol. 74, No. 3 (2007) 242-248. Available here.

Expository papers and surveys

Dilation theory: a guided tour, in Operator Theory: Advances and Applications, Vol. 282 (2021), 551-623.

The isomorphism problem for complete Pick algebras: a survey, with Guy Salomon, in Operator Theory: Advances and ApplicationsVol. 255 (2016), 167-198.

Operator theory and function theory in Drury-Arveson space and its quotients, in Handbook of Operator Theory, editor Daniel Alpay, Springer (2015), 1125-1180.

Dilation theory in finite dimensions: the possible, the impossible and the unknown, with Eliahu Levy, Rocky Mountain Journal of MathematicsVol. 44 No. 1 (2014), 203-221. Available here.

A sneaky proof of the maximum modulus principleThe American Mathematical Monthly, Vol. 120, No. 4 (2013), 359-362. Available here.

Theses

My PhD. Thesis: “Product systems, subproduct systems, and dilation theory of completely positive semigroups”, Orr Moshe Shalit, written under the supervision of Baruch Solel.

My Msc. thesis: “Guided dynamical systems and applications to functional and partial differential equations”, Orr Shalit . Written under the supervision of Boris Paneah.