Related papers: The Kadison-Singer problem in discrepancy theory
In 1959, R.V. Kadison and I.M. Singer asked whether each pure state of the algebra of bounded diagonal operators on $\ell^2$, admits a unique state extension to $B(\ell^2)$. The positive answer was given in June 2013 by A. Marcus, D.…
We present a short proof of the gauge invariant uniqueness theorem for relative Cuntz-Pimsner algebras of C*-correspondences.
The goal of this contribution is to explain the analogy between combinatorial Dyson-Schwinger equations and inductive data types to a readership of mathematical physicists. The connection relies on an interpretation of combinatorial…
We apply to operator algebra theory a monotone selection principle which apparently escaped attention (of operator algebra theorists) so far. This principle relates to the basic order theoretic characterisation of von Neumann algebras given…
We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative…
The universal C*-algebra generated by n projections has been described. As an immediate corollary one obtains structure theorem for a pair of projections and the solution to an associated index problem. This puts the study of a pair of…
The results for meson condensation in the literature vary markedly depending on whether one uses chiral perturbation theory or the current-algebra-plus-PCAC approach. To elucidate the origin of this discrepancy, we re-examine the role of…
We give series solutions to single insertion place propagator-type systems of Dyson--Schwinger equations using binary tubings of rooted trees. These solutions are combinatorially transparent in the sense that each tubing has a…
We study C*-irreducibility of inclusions of reduced twisted group C*-algebras and of reduced group C*-algebras. We characterize C*-irreducibility in the case of an inclusion arising from a normal subgroup, and exhibit many new examples of…
Let \beta : S^n \to S^n, for n = 2k + 1, k \geq 1, be one of the known examples of a non-uniquely ergodic minimal diffeomorphism of an odd dimensional sphere. For every such minimal dynamical system (S^n, \beta) there is a Cantor minimal…
QCD sum rules are useful tools for studying the spectral properties of hadrons; however, assumptions underlying standard sum-rule analyses can lead to inconsistencies with known results of chiral perturbation theory. This possibility is…
Akemann and Weaver (2014) have shown a remarkable extension of Weaver's $KS_r$ Conjecture (2004) in the form of approximate Lyapunov's theorem. This was made possible thanks to the breakthrough solution of the Kadison-Singer problem by…
In this paper, we find all integers $c$ having at least two representations as a difference between linear recurrent sequences. This problem is a pillai problem involving Padovan and Fibonacci sequence. The proof of our main theorem uses…
In this paper, we introduce the countable chain condition for C*-algebras and study its fundamental properties. We show independence from ZFC of the statement that this condition is preserved under the tensor products of C*-algebras.
We study the representation theory and enveloping $C^*$-algebras for Wick analogues of CAR and twisted CAR algebras. The realization of the $C^*$-algebras under consideration as algebras of continuous matrix-functions satisfying certain…
In the $C^*$-algebraic setting the spectrum of any group-like element of a compact quantum group is shown to be a closed subgroup of the one-dimensional torus. A number of consequences of this fact are then illustrated, along with a loose…
We present a systematic, algorithmic method to compute the preimage of elements under the Singer algebraic transfer. Using the lambda algebra and the invariant-theoretic formula of P.H. Chon and L.M. Ha [5], we formulate the preimage search…
The category of modules over a string algebra is equipped with a tensor product defined point-wise and arrow-wise in terms of the underlying quiver. In the present article we investigate how this tensor product interacts with the…
In this paper we prove some uncertainty bounds for commutators and anti-commutators of observables in a $C^*$-algebra. We give a short, elementary proof of Robertson's Standard Uncertaity Principle in this setting. We also prove some other…
Interactions of $a_2, K^*_2, f_2$ and $f_2'$ tensor-mesons with low-energy $\pi, K, \eta, \eta'$ pseudo-scalar mesons are constrained by chiral symmetry. We derive a chiral Lagrangian of tensor mesons in which the tensor mesons are treated…