Positive Operators [electronic resource] / by Charalambos D. Aliprantis, Owen Burkinshaw.

The Order Structure of Positive Operators -- Components, Homomorphisms, and Orthomorphisms -- Topological Considerations -- Banach Lattices -- Compactness Properties of Positive Operators -- Micromechanics and multiscale mechanics of carbon nanotubes-reinforced composites -- Multi-scale analytical methods for complex flows in process engineering: Retrospect and prospect -- Multiscaling effects in low alloy TRIP steels -- Ductile Cr-Alloys with solute and precipitate softening -- A multi-scale approach to crack growth -- Continuum-based and cluster models for nanomaterials -- Segmented multiscale approach by microscoping and telescoping in material science -- Mode I segmented crack model: Macro/symmetry, micro/ anti-symmetry and dislocation/skew-symmetry -- Tensegrity architecture and the mammalian cell cytoskeleton -- Mode II segmented crack model: Macro/skew-symmetry micro/anti-symmetry and dislocation/skew-symmetry -- Microstructure and microhardness in surface-nanocrystalline Al-alloy material -- Grain boundary effects on fatigue damage and material properties: Macro- and micro-considerations -- Coupling and communicating between atomistic and continuum simulation methodologies.

Reprinted by popular demand, this monograph presents a comprehensive study of positive operators between Riesz spaces and Banach lattices. Since the first publication of this book, (Academic Press, 1985), the subject of positive operators and Riesz spaces has found many applications in several disciplines, including social sciences and engineering. It is well known that many linear operators between Banach spaces arising in classical analysis are in fact positive operators. Therefore we study here positive operators in the setting of Riesz spaces and Banach lattices and from both the algebraic and topological points of view. Special emphasis is given to the compactness properties of positive operators and their relations to the order structures of the spaces the operators are acting upon. In order to make the book as self-sufficient as possible, some basic results from the theory of Riesz spaces and Banach lattices are included with proofs where necessary. However, familiarity with the elementary concepts of real analysis and functional analysis is assumed. The book is divided into five chapters, each consisting of nineteen sections all ending with exercises designed to supplement and illustrate the material.