Related papers: A simple proof of Brown's diagonalizability theore…

A new approach to disintegration of measures is presented, allowing one to drop the usually taken separability assumption. The main tool is a result on fibers in the spectrum of algebra of essentially bounded functions established recently…

A very short proof of Kneser's theorem via transversal is given.

We prove an infinitary version of the Brauer-Schur theorem.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

Doob's theorem provides guarantees of consistent estimation and posterior consistency under very general conditions. Despite the limitation that it only guarantees consistency on a set with prior probability 1, for many models arising in…

We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.

In this paper we generalize Brown's spectral distribution measure to a large class of unbounded operators affiliated with a finite von Neumann algebra. Moreover, we compute the Brown measure of all unbounded R-diagonal operators in this…

We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.

In this work the author studies the property close to property of order separability.

In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.

The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…

In this note we prove that the probability measures generated by two generalized grey Brownian motions with different parameters are singular with respect to each other. This result can be interpreted as an extension of the Feldman-H\'ajek…

We consider a family of free multiplicative Brownian motions $b_{s,\tau}$ parametrized by a real variance parameter $s$ and a complex covariance parameter $\tau.$ We compute the Brown measure $\mu_{s,\tau}$ of $ub_{s,\tau },$ where $u$ is a…

Although there are many simple proofs of Jordan's decomposition theorem in the literature (see [1], the references mentioned there, and [2]), our proof seems to be even more elementary. In fact, all we need is the theorem on the dimensions…

We present a new, elementary, dynamical proof of the prime number theorem.

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

We prove the Aharoni Berger Conjecture

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…

This note concerns a one-line diagrammatic proof of the Cayley-Hamilton Theorem. We discuss the proof's implications regarding the "core truth" of the theorem, and provide a generalization. We review the notation of trace diagrams and…

Although in general there is no meaningful concept of factorization in fields, that in free associative algebras (over a commutative field) can be extended to their respective free field (universal field of fractions) on the level of…