Book:
“A First Course in Functional Analysis”, CRC Press, 2017. Publisher’s website. Here is a link to a list of corrections.
Papers:
The papers are organised according to topic, and some papers appear in more than one category. I’m not sure that this organization scheme makes sense any more, maybe the best way to see my publications is to look at my page on scholar.
Click on the article title to reach a free version. The “available here” links lead to the final version of the paper on the publisher’s website.
Topics: multivariable operator theory, operator algebras, noncommutative dynamics, semigroup theory, functional equations/dynamical systems, expository papers and surveys, theses.
Multivariable operator theory
(Several complex variables and operator theory, Hilbert functions spaces and multiplier algebras, dilation theory, operator spaces)
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.
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 D. Ofek and S. Pandey, Journal of Mathematical Analysis and Applications, Vol. 500 Issue 2 (2021), 125140. Available here.
Dilations of unitary tuples, with M. Gerhold, S. Pandey and B. Solel, Journal of the London Mathematical Society, Vol. 104 No. 2 (2021), 2053-2081. Available here.
On the matrix range of random matrices, with M. Gerhold, Journal of Operator Theory, Vol. 85 No. 2 (2021). Available here.
Dilations of q-commuting unitaries, with M. 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 G. Salomon and E. Shamovich, Journal of Functional Analysis, Vol. 278 Issue 7 (2020), 108427. Available here.
Compressions of compact tuples, with B. Passer, Linear Algebra and its Applications, Vol. 564 No. 1 (2019), 264-283. Available here.
Algebras of bounded noncommutative analytic functions on subvarieties of the noncommutative unit ball, with G. Salomon and E. Shamovich, Transactions of the American Mathematical Society, Vol. 370 No. 12 (2018), 8639–8690. Available here.
Minimal and maximal matrix convex sets, with B. Passer and B. 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 Ken Davidson, Adam Dor-On and Baruch Solel, International Mathematics Research Notices, Vol. 2017 Issue 13 (2017), 4069-4130. Available here. Note: 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 Mathematics, Vol. 228 (2011) 167-218. Available here.
Stable polynomial division and essential normality of graded Hilbert modules, Journal of the London Mathematical Society, Vol. 83 Issue 2 (2011) 273-289. Available here.
Operator algebras
(Nonselfadjoint operator algebras, C*-algebras, C*-correspondences, product systems and subproduct systems)
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.
Algebras of noncommutative functions on subvarieties of the noncommutative ball: the bounded and completely bounded isomorphism problem, with G. Salomon and E. Shamovich, Journal of Functional Analysis, Vol. 278 Issue 7 (2020), 108427. 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 G. Salomon and E. Shamovich, Transactions of the American Mathematical Society, Vol. 370 No. 12 (2018), 8639–8690. 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.
The isomorphism problem for some universal operator algebras, with Kenneth R. Davidson and Christopher Ramsey, Advances in Mathematics, Vol. 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.
Noncommutative dynamics
(Semigroups of completely positive maps on operator algebras and their dilations)
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.
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.
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.
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).
Semigroup theory
Bounded perturbations of the Heisenberg commutation relation via dilation theory, with Malte Gerhold, to appear in Proceedings of the American Mathematical Society.
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.
Continuous extension of a densely parameterized semigroup , with Eliahu Levy, Semigroup Forum, Vol. 78, No. 2 (2009) 276-284. Available here.
Functional equations/dynamical systems
Three remarks on a question of Aczel, Aequationes Mathematicae, Vol. 84, No. 3, (2012) 201-205. 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.
On the overdeterminedness of a class of functional equations, Aequationes 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 Applications, Vol. 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 Mathematics, Vol. 44 No. 1 (2014), 203-221. Available here.
A sneaky proof of the maximum modulus principle, The 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.