Shows the natural parallels and connections between the fields of positivity and noncommutative analysis

Informs about the current state in these fields

This volume is dedicated to Ben de Pagter in honour of his 65th birthday

FM.- Ben de Pagter: Curriculum Vitae .- 2-Local automorphisms on AW*-algebras.- Orthosymmetric Archimedean-valued vector lattices.- Arens extensions for polynomials and the Woodbury-Schep formula.- On the endpoints of De Leeuw restriction theorems.- Lebesgue topologies and mixed topologies.- Lattice homomorphisms in harmonic analysis.- Noncommutative Boyd interpolation theorems revisited.- Strict singularity: a lattice approach.- Asymptotics of operator semigroups via the semigroup at infinity.- Markov processes, strong Markov processes and Brownian motion in Riesz spaces.- A solution to the Al-Salam-Chihara moment problem.- The Katowice problem for analysts.- Onefold and twofold Ellis-Gohberg inverse problems for scalar Wiener class functions.- Relatively uniform convergence in partially ordered vector spaces revisited.- Dedekind complete and order continuous Banach C(K)-modules.- Matrix valued Laguerre polynomials.- Weighted Noncommutative Banach Function Spaces.- Majorization for compact and weakly compact polynomials on Banach lattices.- The UMD property for Musielak-Orlicz spaces.- The ls -Boundedness of a Family of Integral Operators on UMD Banach Function Spaces.- Backward stochastic evolution equations in UMD Banach spaces.- On the Lipschitz decomposition problem in ordered Banach spaces and its connections to other branches of mathematics.- Classes of localizable measure spaces.- A residue formula for locally compact noncommutative manifolds.- Regular states and the Regular Algebra Numerical Range.- Bilaplace Eigenfunctions compared with Laplace Eigenfunctions in some special cases.-Representations of the Dedekind completions of spaces of continuous functions.- Joint representation of a Riesz space and its conjugate space.- When do the regular operators between two Banach lattices form a lattice?.- Lexicographic cones and the ordered projective tensor product.