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.

This book presents the fundamental function spaces and their duals, explores operator theory and finally develops the theory of distributions up to significant applications such as Sobolev spaces and Dirichlet problems. Includes an assortment of well formulated exercises, with answers and hints collected at the end of the book.

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. 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.

This book presents nine survey articles addressing topics surrounding positivity, with an emphasis on functional analysis. The book assembles a wide spectrum of research into positivity, providing up-to-date information on topics of current interest. The discussion provides insight into classical areas like spaces of continuous functions, f-algebras, and integral operators. The coverage extends is broad, including vector measures, operator spaces, ordered tensor products, and non-commutative Banach function spaces.

This unique volume brings together state-of-the-art research showing the value of emotions that many believe to be undesirable. Leading investigators explore the functions and benefits of sadness, anxiety, anger, embarrassment, shame, guilt, jealousy, and envy. The role of these emotions in social interactions and relationships is examined, as are cultural differences in how they are valued and expressed. The volume considers how people seek out these feelings in everyday life to improve performance, gain insight, and express cares and commitments. Negative emotions are shown to have an important place in a rich and meaningful life.

The proceedings of the Israeli GAFA seminar on Geometric Aspect of Functional Analysis during the years 2001-2002 follow the long tradition of the previous volumes. They continue to reflect the general trends of the Theory. Several papers deal with the slicing problem and its relatives. Some deal with the concentration phenomenon and related topics. In many of the papers there is a deep interplay between Probability and Convexity. The volume contains also a profound study on approximating convex sets by randomly chosen polytopes and its relation to floating bodies, an important subject in Classical Convexity Theory. All the papers of this collection are original research papers.

This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.

This unique volume brings together state-of-the-art research showing the value of emotions that many believe to be undesirable. Leading investigators explore the functions and benefits of sadness, anxiety, anger, embarrassment, shame, guilt, jealousy, and envy. The role of these emotions in social interactions and relationships is examined, as are cultural differences in how they are valued and expressed. The volume considers how people seek out these feelings in everyday life to improve performance, gain insight, and express cares and commitments. Negative emotions are shown to have an important place in a rich and meaningful life.