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<div>Preface.- Dedication.-&nbsp;Coenraad Christoffel Andries Labuschagne.- Inverse monotonicity of elliptic operators invariational form.- On compact operators between lattice normed spaces.- How to be positive in natural sciences?.- Real positive maps and conditional expectations on operator algebras.- Free vector lattices and free vector lattice algebras.- On disjointness, bands and projections in partially ordered vector spaces.- 101 years of vector lattice theory - a vector lattice-valued Daniell integral.- Ergodicity in Riesz spaces.- Multiplicative representation of real-valued</div><div>bi-Riesz homomorphisms on partially ordered vector spaces.- Orthogonality: An antidote to Kadison's antilattice theorem.- Binary Relations in Mathematical Economics: On Continuity, Additivity and Monotonicity Postulates in Eilenberg, Villegas and DeGroot.- On fixed point theory in partially ordered (quasi-)metric spaces and an application to complexity analysis of algorithms.- Inheritance properties of positive cones induced by subalgebras and quotients of ordered Banach algebras.- Universally complete spaces of continuous functions.- Applications of generalized B -algebras to quantum mechanics.</div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div><div><br></div>

<p>This proceedings volume features selected contributions from the conference Positivity X. The field of positivity deals with ordered mathematical structures and their applications. At the biannual series of Positivity conferences, the latest developments in this diverse field are presented. The 2019 edition was no different, with lectures covering a broad spectrum of topics, including vector and Banach lattices and operators on such spaces, abstract stochastic processes in an ordered setting, the theory and applications of positive semi-groups to partial differential equations, Hilbert geometries, positivity in Banach algebras and, in particular, operator algebras, as well as applications to mathematical economics and financial mathematics. The contributions in this book reflect the variety of topics discussed at the conference. They will be of interest to researchers in functional analysis, operator theory, measure and integration theory, operator algebras, and economics.</p>

<p>Positivity X was dedicated to the memory of our late colleague and friend, Coenraad Labuschagne. His untimely death in 2018 came as an enormous shock to the Positivity community. He was a prominent figure in the Positivity community and was at the forefront of the recent development of abstract stochastic processes in a vector lattice context.</p><br>

Features selected contributions from the conference Positivity X Deals with ordered mathematical structures and their applications Covers a broad spectrum of topics