Capturing the state of the art of the interplay between positivity, noncommutative analysis, and related areas including partial differential equations, harmonic analysis, and operator theory, this volume was initiated on the occasion of the Delft conference in honour of Ben de Pagter's 65th birthday. It will be of interest to researchers in positivity, noncommutative analysis, and related fields.

Contributions by Shavkat Ayupov, Amine Ben Amor, Karim Boulabiar, Qingying Bu, Gerard Buskes, Martijn Caspers, Jurie Conradie, Garth Dales, Marcel de Jeu, Peter Dodds, Theresa Dodds, Julio Flores, Jochen Glück, Jacobus Grobler, Wolter Groenevelt, Markus Haase, Klaas Pieter Hart, Francisco Hernández, Jamel Jaber, Rien Kaashoek, Turabay Kalandarov, Anke Kalauch, Arkady Kitover, Erik Koelink, Karimbergen Kudaybergenov, Louis Labuschagne, Yongjin Li, Nick Lindemulder, Emiel Lorist, Qi Lü, Miek Messerschmidt, Susumu Okada, Mehmet Orhon, Denis Potapov, Werner Ricker, Stephan Roberts, Pablo Román, Anton Schep, Claud Steyn, Fedor Sukochev, James Sweeney, Guido Sweers, Pedro Tradacete, Jan Harm van der Walt, Onno van Gaans, Jan van Neerven, Arnoud van Rooij, Freek van Schagen, Dominic Vella, Mark Veraar, Anthony Wickstead, Marten Wortel, Ivan Yaroslavtsev, and Dmitriy Zanin.

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

Inhalt
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 l*s -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.