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The James space J and the James tree space JT were constructed as counterexamples to several outstanding conjectures in Banach space theory. This book is a compendium of most of the known results about these spaces, frequently taken from the original sources, but presented in a unified and up to date fashion. Generalisations of J and JT are also discussed and other pathological Banach spaces are introduced. Specialists will welcome this book for its drawing together of classical material and recent results. Graduate students should also find that this book offers an excellent introduction to more advanced topics in Banach space theory.
Banach spaces. --- Functions of complex variables --- Generalized spaces --- Topology
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This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. ContentsIntroductionLinear operatorsBasic notations and resultsBasesSemi-groupsDiscrete operator and denseness of the generalized eigenvectorsFrames in Hilbert spacesSummability of seriesν-convergence operatorsΓ-hypercyclic set of linear operatorsAnalytic operators in Béla Szökefalvi-Nagy's senseBases of the perturbed operator T(ε) Frame of the perturbed operator T(ε) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory
Banach spaces. --- Functions of complex variables --- Generalized spaces --- Topology
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Space and time --- Generalized spaces. --- Nonlinear theories. --- Mathematics.
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This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: the elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) spaces. While these topics can be traced back to Banach himself, our primary interest is in the postwar renaissance of Banach space theory brought about by James, Lindenstrauss, Mazur, Namioka, Pelczynski, and others. Their elegant and insightful results are useful in many contemporary research endeavors and deserve greater publicity. By way of prerequisites, the reader will need an elementary understanding of functional analysis and at least a passing familiarity with abstract measure theory. An introductory course in topology would also be helpful; however, the text includes a brief appendix on the topology needed for the course.
Banach spaces. --- Banach, Espaces de --- Functions of complex variables --- Generalized spaces --- Topology
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The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich - one of the leading category theorists of the world - to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader
Categories (Mathematics) --- Topological spaces --- Metric spaces --- Topology --- Spaces, Metric --- Generalized spaces --- Set theory --- Spaces, Topological
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The relatively new concepts of the Henstock-Kurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The Henstock-Kurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.
Banach spaces. --- Integrals. --- Calculus, Integral --- Functions of complex variables --- Generalized spaces --- Topology
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This book presents a theory motivated by the spaces LP, 0 ≤ p < l. These spaces are not locally convex, so the methods usually encountered in linear analysis (particularly the Hahn-Banach theorem) do not apply here. Questions about the size of the dual space are especially important in the non-locally convex setting, and are a central theme. Several of the classical problems in the area have been settled in the last decade, and a number of their solutions are presented here. The book begins with concrete examples (lp, LP, L0, HP) before going on to general results and important counterexamples. An F-space sampler will be of interest to research mathematicians and graduate students in functional analysis.
Function spaces. --- Metric spaces. --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Spaces, Function --- Functional analysis
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Denne bog praesenterer den studerende for den indledende lineaere algebras problemstillinger og metoder. Ved at gennemarbejde bogens eksempler sikres den studerende både en forståelse af den underliggende teori og en opbygning af forbedret regnefaerdighed. På den måde er bogen et vaerdifuldt vaerktoj for enhver studerende, der skal til at give sig i kast med den lineaere algebras forskellige udfordringer.
Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology
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Linear algebra is a fundamental area of mathematics, and arguably the most powerful mathematic tool ever deployed. This book uses numerous examples, question and answer sections, and historical biographies to provide an introduction to linear algebra for undergraduates in mathematics, the physical sciences and engineering.
Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology
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Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincaré inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincaré inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincaré inequalities under Gromov-Hausdorff convergence, and the Keith-Zhong self-improvement theorem for Poincaré inequalities.
Metric spaces. --- Sobolev spaces. --- Spaces, Sobolev --- Function spaces --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology
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