Space in Theory


Book Description

Space in Theory: Kristeva, Foucault, Deleuze seeks to give a detailed but succinct overview of the role of spatial reflection in three of the most influential French critical thinkers of recent decades. It proposes a step-by-step analysis of the changing place of space in their theories, focussing on the common problematic all three critics address, but highlighting the significant differences between them. It aims to rectify an unaccountable absence of detailed analysis to the significance of space in their work up until now. Space in Theory argues that Kristeva, Foucault and Deleuze address the question: How are meaning and knowledge produced in contemporary society? What makes it possible to speak and think in ways we take for granted? The answer which all three thinkers provide is: space. This space takes various forms: psychic, subjective space in Kristeva, power-knowledge-space in Foucault, and the spaces of life as multiple flows of becoming in Deleuze. This book alternates between analyses of these thinkers’ theoretical texts, and brief digressions into literary texts by Barrico, de Beauvoir, Beckett, Bodrožić or Bonnefoy, via Borges, Forster, Gide, Gilbert, Glissant, Hall, to Kafka, Ondaatje, Perec, Proust, Sartre, Warner and Woolf. These detours through literature aim to render more concrete and accessible the highly complex conceptulization of contemporary spatial theory. This volume is aimed at students, postgraduates and researchers interested in the areas of French poststructuralist theory, spatial reflection, or more generally contemporary cultural theory and cultural studies.




Space and Social Theory


Book Description

The importance of the spatial dimension of the structure, organization and experience of social relations is fundamental for sociological analysis and understanding. Space and Social Theory is an essential primer on the theories of space and inherent spatiality, guiding readers through the contributions of key and influential theorists: Marx, Simmel, Lefebvre, Harvey and Foucault. Giving an essential and accessible overview of social theories of space, this books shows why it matters to understand these theorists spatially. It will be of interest to upper level students and researchers of social theory, urban sociology, urban studies, human geography, and urban politics.




Introduction to Operator Space Theory


Book Description

An introduction to the theory of operator spaces, emphasising applications to C*-algebras.




Banach Space Theory


Book Description

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.




Scale-Space Theory in Computer Vision


Book Description

The problem of scale pervades both the natural sciences and the vi sual arts. The earliest scientific discussions concentrate on visual per ception (much like today!) and occur in Euclid's (c. 300 B. C. ) Optics and Lucretius' (c. 100-55 B. C. ) On the Nature of the Universe. A very clear account in the spirit of modern "scale-space theory" is presented by Boscovitz (in 1758), with wide ranging applications to mathemat ics, physics and geography. Early applications occur in the cartographic problem of "generalization", the central idea being that a map in order to be useful has to be a "generalized" (coarse grained) representation of the actual terrain (Miller and Voskuil 1964). Broadening the scope asks for progressive summarizing. Very much the same problem occurs in the (realistic) artistic rendering of scenes. Artistic generalization has been analyzed in surprising detail by John Ruskin (in his Modern Painters), who even describes some of the more intricate generic "scale-space sin gularities" in detail: Where the ancients considered only the merging of blobs under blurring, Ruskin discusses the case where a blob splits off another one when the resolution is decreased, a case that has given rise to confusion even in the modern literature.




Function Theory and ℓp Spaces


Book Description

The classical ℓp sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces ℓpA of analytic functions whose Taylor coefficients belong to ℓp. Relations between the Banach space ℓp and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of ℓpA and a discussion of the Wiener algebra ℓ1A. Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.




Henri Lefebvre's Critical Theory of Space


Book Description

Henri Lefebvre's Critical Theory of Space offers a rigorous analysis and revival of Lefebvre’s works and the context in which he produced them. Biagi traces the historical-critical time-frame of Lefebvre's intellectual investigations, bringing to light a theoretical constellation in which historical methods intersect with philosophical and sociological issues: from Marxist political philosophy to the birth of urban sociology; from rural studies to urban and everyday life studies in the context of capitalism. Examining Lefebvre’s extended investigations into the urban sphere as well as highlighting his goal of developing a “general political theory of space” and of innovating Marxist thought, and clarifying the various (more or less accurate) meanings attributed to Lefebvre's concept of the “right to the city” (analysed in the context of the French and international sociological and philosophical-political debate), Henri Lefebvre's Critical Theory of Space ultimately brings the contours of Lefebvre’s innovative perspective—itself developed at the end of the “short twentieth century”—back into view in all its richness and complexity.




Topics in Banach Space Theory


Book Description

This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews




An Introduction to Banach Space Theory


Book Description

Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.




Standing in Space


Book Description