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It is shown that there are domains that maximise the expected lifetime of Brownian motion over all simply connected domains of given inradius and all starting points.
In this paper we study some important structural properties of weak orthomorphisms. Some new results of such operators are presented.
A dual Banach algebra is a Banach algebra that is a dual space, with the multiplication being separately weak * -continuous. We show that given a unital dual Banach algebra A , we can find a reflexive Banach space E , and an isometric, weak * -weak * -continuous homomorphism π : A → B ( E ) such...
Conditions ensuring that a finite group G is abelian are given in terms of element centralisers and automorphisms of G .
Let 픻 be the open unit disk in the complex plane and ϕ : 픻 → 픻 as well as ψ : 픻 → ℂ be analytic maps. For a holomorphic function ƒ on 픻 the weighted composition operator C ϕ,ψ is defined by ( C ϕ,ψ ƒ)( z ) = ψ( z )ƒ(ϕ( z )) for every z ∈ 픻. We characterize when weighted composition operators...
We describe completely the ternary isomorphisms between abelian Hilbert ternary algebras.
We obtain a number of positive solutions to the following problem: if Ω is a domain in a locally convex space E, X and Y are Banach spaces with Y ⊂ X and quotient mapping π : X → X / Y , and ƒ : Ω → X / Y is holomorphic, does there exist a holomorphic mapping h : Ω → X such that ƒ = π º h ? The...
The commutativity degree of a finite group is the probability that two randomly chosen group elements commute. The main object of this paper is to obtain a characterisation for all finite groups of odd order with commutativity degree greater than or equal to .
First we compute explicitly the norm of 2-homogeneous polynomials on the 2-dimensional real predual of the Lorenz sequence space d * (1,w) 2 . Using these computations, we classify the extreme points of the unit ball of the space of 2-homogeneous polynomials on d * (1, w ) 2 .
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