Let M be a type I von Neumann algebra with the center Z and a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ -measurable operators affiliated with M. We prove that any Z-linear derivation on L(M, τ) is inner and hence automatically continuous in the measure topology. If the lattice of projections from Z is atomic then any derivation on L(M, τ) is Z-linear. This implies...

Abstract. Let R be a 2-torsion free ring with identity. In this paper, first we prove that any Jordan left derivation (hence, any left derivation) on the full matrix ringMn(R) (n 2) is identically zero, and any generalized left derivation on this ring is a right centralizer. Next, we show that if R is also a prime ring and n 1, then any Jordan left derivation on the ring Tn(R) of all n×n uppe...

The goal of the paper was the analysis of patients over the age of 60 suffering from the urinary bladder cancer that underwent radical surgical treatment of the urinary bladder and establishing urine derivation. In the 1972-2008 period 2405 patients with the urinary bladder cancer were treated, 296 (12.3%) of whom underwent radical surgical treatment. The average age was between 60 and 80 years...

In a series of papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. However, for certain combinations of the masses and the orbital elements, the secular part of the solution failed. In the present paper, we derive a new solution for the secular part of the inner eccentricity, which corrects the pre...

In a noncommutative torus, effect of perturbation by inner derivation on the associated quantum stochastic process and geometric parameters like volume and scalar curvature have been studied. Cohomological calculations show that the above perturbation produces new spectral triples. Also for the Weyl C-algebra, the Laplacian associated with a natural stochastic process is obtained and associated...

We show that, for every ultraprime Banach algebra A, there exists a positive number γ satisfying γ‖a+Z(A)‖ ≤ ‖Da‖ for all a in A, where Z(A) denotes the centre of A and Da denotes the inner derivation on A induced by a. Moreover, the number γ depends only on the “constant of ultraprimeness” of A.

In analogy to the subject of Gaussian integration formulas we present an overview of some Gaussian summation formulas. The derivation involve polynomials that are orthogonal under discrete inner products and the resulting formulas are useful as a numerical device for summing fairly general series. Several illuminating examples are provided in order to present various aspects of this not very we...

In a noncommutative torus, effect of perturbation by inner derivation on the associated quantum stochastic process and geometric parameters like volume and scalar curvature have been studied. Cohomological calculations show that the above perturbation produces new spectral triples. Also for the Weyl C∗-algebra, the Laplacian associated with a natural stochastic process is obtained and associate...

An Einstein nilradical is a nilpotent Lie algebra, which can be the nilradical of a metric Einstein solvable Lie algebra. The classification of Riemannian Einstein solvmanifolds (possibly, of all noncompact homogeneous Einstein spaces) can be reduced to determining, which nilpotent Lie algebras are Einstein nilradicals and to finding, for every Einstein nilradical, its Einstein metric solvable ...

We study a class of matrix function algebras, here denoted T (Cn). We introduce a notion of point derivations, and classify the point derivations for certain finite dimensional representations of T (Cn). We use point derivations and information about n×n matrices to show that every T (Cn)-valued derivation on T (Cn) is inner. Certain matrix function algebras arise in some standard constructions...