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Operator theory --- Banach lattices --- Categories (Mathematics) --- Linear operators --- Positive operators --- Operators, Positive --- Linear maps --- Maps, Linear --- Operators, Linear --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Lattices, Banach --- Banach algebras --- Lattice theory --- Linear operators. --- Lattice theory. --- Catégories (mathématiques) --- Treillis, Théorie des. --- Opérateurs linéaires.
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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.
Teoria d'operadors --- Espais topològics ordenats --- Espais topològics --- Teoria dels operadors --- Anàlisi funcional --- Àlgebres d'operadors --- Equacions d'evolució no lineal --- Operadors diferencials --- Operadors integrals --- Operadors lineals --- Operadors no lineals --- Operadors pseudodiferencials --- Semigrups d'operadors --- Operator theory --- Ordered topological spaces --- Positive operators --- Operators, Positive --- Linear operators --- Spaces, Ordered topological --- Topological spaces
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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.
Positive operators. --- Operators, Positive --- Linear operators --- Computer science. --- Global analysis (Mathematics). --- Mathematics. --- Mathematics of Computing. --- Analysis. --- Applications of Mathematics. --- Game Theory, Economics, Social and Behav. Sciences. --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Informatics --- Computer science—Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Game theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis
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Locally compact semi-algebras
Banach algebras. --- Spectral theory (Mathematics) --- Linear operators. --- Positive operators. --- Operators, Positive --- Linear operators --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras --- Algèbres topologiques. --- Banach, Algèbres de --- Opérateurs linéaires. --- Algèbres topologiques. --- Banach, Algèbres de --- Opérateurs linéaires. --- Locally compact semi-algebras. --- Locally compact spaces.
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"In this monograph, we review the theory and establish new and general results regarding spreading properties for heterogeneous reaction-diffusion equations. These are concerned with the dynamics of the solution starting from initial data with compact support. The nonlinearity f is of Fisher-KPP type, and admits 0 as an unstable steady state and 1 as a globally attractive one (or, more generally, admits entire solutions , where is unstable and is globally attractive). Here, the coefficients are only assumed to be uniformly elliptic, continuous and bounded in . To describe the spreading dynamics, we construct two non-empty star-shaped compact sets such that for all compact set (resp. all closed set , one has lim . The characterizations of these sets involve two new notions of generalized principal eigenvalues for linear parabolic operators in unbounded domains. In particular, it allows us to show that and to establish an exact asymptotic speed of propagation in various frameworks. These include: almost periodic, asymptotically almost periodic, uniquely ergodic, slowly varying, radially periodic and random stationary ergodic equations. In dimension N, if the coefficients converge in radial segments, again we show that and this set is characterized using some geometric optics minimization problem. Lastly, we construct an explicit example of non-convex expansion sets"--
Reaction-diffusion equations. --- Differential equations, Parabolic --- Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions. --- Partial differential equations -- Qualitative properties of solutions -- Homogenization; equations in media with periodic structure. --- Partial differential equations -- Parabolic equations and systems -- Reaction-diffusion equations. --- Partial differential equations -- Qualitative properties of solutions -- Maximum principles. --- Partial differential equations -- Parabolic equations and systems -- Second-order parabolic equations. --- Partial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theory. --- Operator theory -- Special classes of linear operators -- Positive operators and order-bounded operators. --- Calculus of variations and optimal control; optimization -- Hamilton-Jacobi theories, including dynamic programming -- Viscosity solutions. --- Asymptotic theory.
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This book contains nine well-organized survey articles by leading researchers in positivity, with a strong emphasis on functional analysis. It provides insight into the structure of classical spaces of continuous functions, f-algebras, and integral operators, but also contains contributions to modern topics like vector measures, operator spaces, ordered tensor products, non-commutative Banach function spaces, and frames. Contributors: B. Banerjee, D.P. Blecher, K. Boulabiar, Q. Bu, G. Buskes, G.P. Curbera, M. Henriksen, A.G. Kusraev, J. Mart??-nez, B. de Pagter, W.J. Ricker, A.R. Schep, A. Tri
Ordered algebraic structures. --- Vector valued functions. --- Functional analysis. --- Positive operators. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- Operators, Positive --- Linear operators --- Functions, Vector --- Functions, Vector valued --- Functional analysis --- Functions of real variables --- Global analysis (Mathematics). --- Algebra. --- Operator theory. --- Cell aggregation --- Economics. --- Analysis. --- Order, Lattices, Ordered Algebraic Structures. --- Functional Analysis. --- Operator Theory. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Economics, general. --- Mathematics. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Mathematics --- Mathematical analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Manifolds (Mathematics). --- Complex manifolds. --- Management science. --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- 517.1 Mathematical analysis
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