R. Nagel & U. Schlotterbeck 
Aspects of Positivity in Functional Analysis [PDF ebook] 

The contributions collected in this volume exhibit the increasingly wide spectrum of applications of abstract order theory in analysis and show the possibilities of order-theoretical argumentation.The following areas are discussed: potential theory, partial differential operators of second order, Schrodinger operators, theory of convexity, one-parameter semigroups, Lie algebras, Markov processes, operator-algebras, noncommutative integration and geometry of Banach spaces.