Related papers: A noncommutative Bishop peak interpolation-set the…
Peak interpolation is concerned with a foundational kind of mathematical task: building functions in a fixed algebra $A$ which have prescribed values or behaviour on a fixed closed subset (or on several disjoint subsets). In this paper we…
We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective.
We prove the Complete nontrivial cycle-intersection theorem for systems of permutations.
We prove an interpolation theorem for bounded free holomorphic functions.
Using the correspondence between a cycle up-down permutation and a pair of matchings, we give a combinatorial proof of the enumeration of alternating permutations according to the given peak set.
We prove Union-Closed sets conjecture.
We formulate and prove a version of the celebrated Coifman-Rochberg-Weiss commutator theorem for the real method of interpolation
We prove a version of the classical 'generic smoothness' theorem with smooth varieties replaced by non-commutative resolutions of singular varieties. This in particular implies a non-commutative version of the Bertini theorem.
The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem with fast decreasing coefficient, as well as a new modification of the corresponding interpolation formula applicable for general type non-vanishing bounded…
We prove the complete intersection theorem and complete nontrivial-intersection theorem for systems of set partitions
We prove a noncommutative version of the John-Nirenberg theorem for nontracial filtrations of von Neumann algebras. As an application, we obtain an analogue of the classical large deviation inequality for elements of the associated $BMO$…
We prove the non-commutative Laurent phenomenon for two variables.
We prove a combination theorem for PD(n)-pairs.
We construct a class of noncommutative spectra and give the basic properties of the class of noncommutative spectra.
Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…
We prove a Boyd-type interpolation result for noncommutative maximal operators of restricted weak type. Our result positively answers an open question posed recently by Bekjan, Chen and Osekowski. As a special case, we find a restricted…
New examples of noncommutative 4-spheres are introduced.
In this article, using generalized derivations, we obtain a simple idea to prove the non-commutative Newton binomial formula in unital algebras and then, we extend that formula to non-unital algebras. Additionally, we establish the…
We show that the independent set sequence of a bipartite graph need not be unimodal.
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.