We give a complete description of ring isomorphisms between algebras measurable operators affiliated with von Neumann type II$_1.$

It is proved that bounded linear operators on Banach spaces of “cadlag” functions are measurable with respect to the Borel σ-algebra associated with the Skorokhod topology.

For every selfadjoint operator T in the Hilbert space H, f(T) makes sense not only in the obvious case where / is a polynomial but also if / is just measurable, and if fn(x)-+f(x) for all x£R (with (/,) bounded) then fn(T)-+f(T) weakly, i.e. <fn(T)£9i)+<f(T)£9ti)V£9fiCH. Moreover the set {f(T)9 f measurable} is the set of all operators S in H invariant under all unitary transformations of H whi...

Some basic concepts are discussed to derive renormalisation factors of local lattice operators relevant to deep inelastic structure functions and to other measurable quantities. These Z factors can be used to relate matrix elements measured by lattice techniques to their continuum counterparts. We discuss the O(a) improvement of point and one–link lattice quark operators. Suitable bases of impr...

This article is divided into two parts. In the first part we present a general theory of the dyadic lattices. In the second part we show several applications of this theory to harmonic analysis: a decomposition of an arbitrary measurable function in terms of its local mean oscillations, and a pointwise bound of CalderónZygmund operators by sparse operators. Table of

The study of random fixed points has been an active area of contemporary research in mathematics. Some of the recent works in this field are noted in [1, 2, 3, 11]. In particular, random iteration schemes leading to random fixed points were introduced in [3]. After that, random iterations for finding solutions of random operator equations and fixed points of random operators have been discussed...

Abstract. Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on Rn. In particular, in the case when n = 2 they obtained Gaussian upper bound estimates for the heat kernel without imposing further assumption on the coefficients. We study the fundamental solutions of the systems of second o...