We introduce the notions of measurable and strong measurable sensitivity, which are measure-theoretic versions of the conditions of sensitive dependence on initial conditions and strong sensitive dependence on initial conditions, respectively. Strong measurable sensitivity is a consequence of light mixing, implies that a transformation has only finitely many eigenvalues, and does not exist in t...

In the present paper we continue the study of the structure of a Banach algebra B(A,Tg) generated by a certain Banach algebra A of operators acting in a Banach space D and a group {Tg}g∈G of isometries of D such that TgAT −1 g = A. We investigate the interrelations between the existence of the expectation of B(A,Tg) onto A, metrical freedom of the automorphisms of A induced by Tg and the dual a...

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...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

A natural L∞ functional calculus for an absolutely continuous contraction is investigated. It is harmonic in the sense that for such a contraction and any bounded measurable function φ on the circle, the image can rightly be considered as φ̂(T ), where φ̂ is the solution of the Dirichlet problem for the disk with boundary values φ. The main result shows that if the functional calculus is isometri...

We give an example of a measurable set E ⊆ R such that the set E ′ = {(x, y) : x + y ∈ E} is not in the σ-algebra generated by the rectangles with measurable sides. We also prove a stronger result that there exists an analytic (Σ11) set E such that E ′ is not in the σ-algebra generated by rectangles whose horizontal side is measurable and vertical side is arbitrary. The same results are true wh...

Let G be a connected Lie group with Lie algebra g and a 1 ; : : : ; a d 0 an algebraic basis of g. Further let A i denote the generators of left translations, acting on the L p-spaces L p (G ; dg) formed with left Haar measure dg, in the directions a i. We consider second-order operators

We discuss inverse spectral theory for singular differential operators on arbitrary intervals (a, b) ⊆ R associated with rather general differential expressions of the type τf = 1 r ( − ( p[f ′ + sf ] )′ + sp[f ′ + sf ] + qf ) , where the coefficients p, q, r, s are Lebesgue measurable on (a, b) with p−1, q, r, s ∈ Lloc((a, b); dx) and real-valued with p 6= 0 and r > 0 almost everywhere on (a, ...

Effective Lagrangians with dimension-six operators are widely used to analyse Higgs and other electroweak data. We show how to build a basis of operators such that each operator is linked to a coupling which is well measured or will be in the future. We choose a set of couplings such that the correspondence is one-to-one. The usual arbitrary coefficients in front of operators can be constrained...