Related papers: Testing von Neumann inequalities with nilpotent ma…
We announce some new results regarding the classification problem for separable von Neumann algebras. Our results are obtained by applying the notion of Borel reducibility and Hjorth's theory of turbulence to the isomorphism relation for…
The nonlinear eigen-problem $ Ax+F(x)=\lambda x$ is studied where $A$ is an $n\times n$ irreducible Stieltjes matrix. Under certain conditions, this problem has a unique positive solution. We show that, starting from a multiple of the…
We show that standard deviation $\s$ satisfies the Leibniz inequality $\s(fg) \leq \s(f)\|g\| + \|f\|\s(g)$ for bounded functions f, g on a probability space, where the norm is the supremum norm. A related inequality that we refer to as…
In this paper, we use the tools of nonabelian duality to formulate and prove a far-reaching generalization of the Stone-von Neumann Theorem to modular representations of actions and coactions of locally compact groups on elementary $…
We study inequalities connecting a product of uniform norms of polynomials with the norm of their product. Generalizing Gel'fond-Mahler inequality for the unit disk and Kneser-Borwein inequality for the segment $[-1,1]$, we prove an…
The assignment (nonstable K_0-theory), that to a ring R associates the monoid V(R) of Murray-von Neumann equivalence classes of idempotent infinite matrices with only finitely nonzero entries over R, extends naturally to a functor. We prove…
We prove an interpolation formula for the values of certain $p$-adic Rankin--Selberg $L$-functions associated to non-ordinary modular forms.
Let $B$ be a nilpotent matrix and suppose that its Jordan canonical form is determined by a partition $\lambda$. Then it is known that its nilpotent commutator $N_B$ is an irreducible variety and that there is a unique partition $\mu$ such…
We prove that the noncommutative Lorentz norm (associated to a semifinite von Neumann algebra) of a propagator of the form $\varphi(|\mathscr{L}|)$ can be estimated if the modulus of the Borel function $\varphi$ is bounded by a continuous…
We give a new and elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the…
Inspired by Lehner's results on exchangeability systems we define `weak conditional freeness' and `conditional freeness' for stationary processes in an operator algebraic framework of noncommutative probability. We show that these two…
We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup. We prove our results in a general semi-finite von Neumann algebra. We find…
Noether's problem is classical and very important problem in algebra. It is an intrinsically interesting problem in invariant theory, but with far reaching applications in the sutdy of moduli spaces, PI-algebras, and the Inverse problem of…
Motivated by a recent result on finite-dimensional Hilbert spaces, we prove a Jensen's inequality for partial traces in semifinite von Neumann algebras. We also prove a similar inequality in the framework of general (non-tracial) von…
The classical Julia-Wolff-Carath{\'e}odory Theorem characterizes the behaviour of the derivative of an analytic self-map of a unit disc or of a half-plane of the complex plane at certain boundary points. We prove a version of this result…
In this paper we present a generalization of the Radon-Nikodym theorem proved by Pedersen and Takesaki. Given a normal, semifinite and faithful (n.s.f.) weight $\phi$ on a von Neumann algebra M and a strictly positive operator $\delta$,…
Prompted by an observation about the integral of exponential functions of the form $f(x)=\lambda e^{\alpha x}$, we investigate the possibility to exactly integrate families of functions generated from a given function by scaling or by…
In this paper we are concerned with a Gordan-type theorem involving an arbitrary number of inequality functions. We not only state its validity under a weak convexity assumption on the functions, but also show it is an optimal result. We…
By an example we show that Olaf Mueller's assertion about his new theorems being able to give anew some classical results previously obtained via applications of Nash--Moser type theorems is unfounded. We also give another example…
The Carath\'{e}odory problem in the $N$-variable non-commutative Herglotz--Agler class and the Carath\'{e}odory--Fej\'{e}r problem in the $N$-variable non-commutative Schur--Agler class are posed. It is shown that the Carath\'{e}odory…