Research interests

Shalits_NahalKelahMay2017

My research is in and around the fields of operator algebras, operator theory and functional analysis.

Currently I am involved with projects on

  • Completely positive maps and semigroups: interpolation of CP maps, dilations, product systems, superprodcut systems and subproduct systems, C* and von Neumann correspondences.
  • Multivariable operator theory: dilation theory, matrix ranges and matrix convexity, model theory, noncommutative function theory,  noncommutative varieties.
  • Operator systems, non-selfadjoint operator algebras and C*-algebras.
  • Hilbert spaces and algebras of holomorphic functions (classical as well as noncommutative) and operators that act on them.

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Research grants:

  1. GTIIT – Technion Seed Grant (2026 — 2027).
  2. ISF Research Grant No. 431/20 (2020 — 2025) proposal.
  3. ISF Research Grant No. 195/16 (2016 — 2020) proposal.
  4. GIF Research Grant No. 2297-2282.6/201 (2013) proposal abstract.
  5. The Gerald Schwartz & Heather Reisman Foundation for Technion-UWaterloo cooperation (2015 – 2016).
  6. ISF Research Grant No. 474/12 (2012 — 2016) proposal abstract.
  7. Marie-Curie CIG Grant No. 321749 (2012—2016) proposal.

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Some research statements from various stages:

Here is a bird’s eye view of my research written in 2025 for some grant proposal.

Here is a “research story” of how I was led to study NC function theory, written in 2025.

Here is a Research Statement, highlighting my research between 2017 and 2023.

Here is a Research Statement, summarizing the central themes of my research up to June 2017.

Here is a Research Report prepared for the workshop “Hilbert Modules and Complex Geometry”, in Oberwolfach, April 2014.