<p>This book is the English translation of the new and expanded version of Bourbaki's "Espaces vectoriels topologiques". Chapters 1 and 2 contain the general definitions and a thorough study of convexity; they are organized around the basic theorems (closed graph, Hahn-Banach and Krein-Milman), and differ only by minor changes from those of older editions. Chapter 3 and 4 have been substantially rewritten; the order of exposition has been modified and a number of notions and results have been inserted, whose importance emerged in the last twenty years. Bornological spaces are introduced together with barrelled ones; almost every space of practical use today belongs in fact to these two categories, which have good stability properties, and in which the basic theorems (the Banach-Steinhaus theorem for example) apply. Recent results on the completion of a dual space (Grothendieck theorem) or on the continuity of linear maps with measurable graphs are treated. An important place is devoted to properties of Fréchet spaces and of their dual spaces, to compactness criteria (Eberlein-Smullian) and to the existence of fixed points for groups of linear maps. Chapter 5 is devoted to Hilbert spaces; it includes in particular the spectral decomposition of Hilbert-Schmidt operators and the construction of symmetric and exterior powers of Hilbert spaces, whose applications are of growing importance. At the end, an appendix restates the principal results obtained in the case of normed spaces, providing convenient references. The book addresses all mathematicians and physicists interested in a structural presentation of contemporary mathematics.</p>

Topological Vectors Spaces: Elements of Mathematics

Science & Math

Bourbaki, N.

Madan, S.

Eggleston, H.G.

Mathematics

Springer, Verlag

Algebra I: Chapters 1-3 (Elements of Mathematics) (English and French Edition)

<p>Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements.\nLe Livre de Théories spectrales est consacré à l'étude des algèbres normées et de leurs applications. Le premier chapitre met en place la théorie fondamentale des algèbres de Banach et des algèbres stellaires. Nous y présentons l'équivalence de catégories entre algèbres stellaires commutatives et espaces topologiques localement compacts, ainsi que le calcul fonctionnel holomorphe en plusieurs variables dans une algèbre de Banach commutative.<br />
La transformation de Fourier, qui est l'un des outils mathématiques les plus universels, est étudiée au second chapitre, dans le cadre des groupes localement compacts commutatifs.<br />
Le texte est complété par de nombreux exercices.\nCes deux chapitres forment une édition entièrement refondue de l'édition de 1967.\nThe Elements of Mathematics of Nicolas Bourbaki have the goal of giving a rigorous and systematic presentation of mathematics starting from the foundations, without prerequisites. The book of Spectral Theories is devoted to the study of normed algebras and their applications. The first chapter establishes the basic theory of Banach algebras and C*-algebras. We present the equivalence of categories between commutative C*-algebras and locally compact topological spaces, as well as the holomorphic functional calculus in several variables in a commutative Banach algebra.The Fourier transform, which is one of the most universal mathematical tools, is studied in the second chapter, in the context of locally compact commutative topological groups.\nThe text is accompanied by many exercices.<br />
These two chapters are completely updated new versions of the 1967 original edition.\nFrom the Back Cover\nLes Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements.\nLe Livre de Théories spectrales est consacré à l'étude des algèbres normées et de leurs applications. Le premier chapitre met en place la théorie fondamentale des algèbres de Banach et des algèbres stellaires. Nous y présentons l'équivalence de catégories entre algèbres stellaires commutatives et espaces topologiques localement compacts, ainsi que le calcul fonctionnel holomorphe en plusieurs variables dans une algèbre de Banach commutative.<br />
La transformation de Fourier, qui est l'un des outils mathématiques les plus universels, est étudiée au second chapitre, dans le cadre des groupes localement compacts commutatifs.Le texte est complété par de nombreux exercices.\nCes deux chapitres forment une édition entièrement refondue de l'édition de 1967.</p>

Théories spectrales: Chapitres 1 et 2 (French Edition)

Springer

<p>This book is an English translation of an entirely revised version of the 1958 edition of the eighth chapter of the book Algebra, the second Book of the Elements of Mathematics. <div> <div><br /></div> <div>It is devoted to the study of certain classes of rings and of modules, in particular to the notions of Noetherian or Artinian modules and rings, as well as that of radical.</div> <div><br /></div> <div>This chapter studies Morita equivalence of module and algebras, it describes the structure of semisimple rings.&nbsp; Various Grothendieck groups are defined that play a universal role for module invariants.</div> <div>The chapter also presents two particular cases of algebras over a field.&nbsp; The theory of central simple algebras is discussed in detail; their classification involves the Brauer group, of which several</div> <div>descriptions are given.&nbsp; Finally, the chapter considers group algebras and applies the general theory to representations of finite groups.</div> <div><br /></div> <div>At the end of the volume, a historical note taken from the previous edition recounts the evolution of many of the developed notions.</div> <div><br /></div> </div></p>

Algebra: Chapter 8

<p>Les Éléments de mathématique de Nicolas Bourbaki ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements.\nCe second volume, inédit, du Livre consacré aux Théories spectrales a pour thème les propriétés spectrales des applications linéaires.\nLe chapitre 3 étudie les applications linéaires compactes entre espaces vectoriels topologiques et la théorie de la perturbation par addition d'une application linéaire compacte, en particulier la théorie de Fredholm. Il se poursuit par la description du spectre d'un endomorphisme compact d'un espace de Banach, notamment les notions de spectre sensible et de spectre essentiel. On y démontre le théorème de Krein--Rutman.\nLe chapitre 4 contient les résultats fondamentaux de la théorie spectrale hilbertienne : opérateurs compacts et nucléaires, endomorphismes normaux, opérateurs partiels normaux. On y trouve également un exposé concis des distributions et distributions tempérées.\nEnfin, le chapitre 5 aborde l'étude des représentations unitaires des groupes topologiques (constructions élémentaires, lemme de Schur, représentations de carré intégrable modulo le centre, classes de représentations irréductibles). On y développe aussi la théorie des fonctions de type positif et on y démontre le théorème fondamental de Peter--Weyl.\nLe texte est complété par de nombreux exercices et par une note historique portant sur le contenu des chapitres 1 à 5.</p>

Théories spectrales: Chapitres 3 à 5 (French Edition)

<p>This is a softcover reprint of chapters four through seven of the 1990 English translation of the revised and expanded version of Bourbaki's Algebre. Much material was added or revised for this edition, which thoroughly establishes the theories of commutative fields and modules over a principal ideal domain.</p>

Algebra II: Chapters 4 - 7 (Elements of Mathematics)

Computers & Technology

Computer Science

<p><p>Nicolas Bourbaki is a pseudonym</p> <p>under which a group of French 20th</p> <p>century mathematicians wrote a series of books with the aim of reformulating mathematics on an extremely abstract and formal but self-contained</p></p>

Séminaire Bourbaki: Vol. 1971 /72. Exposés 400 - 417 (Lecture Notes in Mathematics, 317) (French Edition)

This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 studies valuation (of any rank), and the last chapter focuses on divisors (Krull, Dedekind, or factorial domains) with a final section on modules over integrally closed Noetherian domains, not usually found in textbooks. Useful exercises appear at the ends of the chapters.

Commutative Algebra: Chapters 1-7

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

<p><strong>Integration</strong> is the sixth and last of the books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology and  Topological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author's Théories Spectrales, an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.</p> <p>The first volume of the English translation comprises Chapters 1-6; the present volume completes the translation with the remaining Chapters 7-9.</p> <p>Chapters 1-5 received very substantial revisions in a second edition, including changes to some fundamental definitions. Chapters 6-8 are based on the first editions of Chapters 1-5. The English edition has given the author the opportunity to correct misprints, update references, clarify the concordance of Chapter 6 with the second editions of Chapters 1-5, and revise the definition of a key concept in Chapter 6 (measurable equivalence relations).</p>

Integration II: Chapters 7–9 (Elements of Mathematics)

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Books by Bourbaki, N.

See the best price to sell, buy, or rent books by Bourbaki, N.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Topological Vectors Spaces: Elements of Mathematics

Algebra I: Chapters 1-3 (Elements of Mathematics) (English and French Edition)

Théories spectrales: Chapitres 1 et 2 (French Edition)

Algebra: Chapter 8

Algebra: Chapter 8

Théories spectrales: Chapitres 3 à 5 (French Edition)

Algebra II: Chapters 4 - 7 (Elements of Mathematics)

Séminaire Bourbaki: Vol. 1971 /72. Exposés 400 - 417 (Lecture Notes in Mathematics, 317) (French Edition)

Commutative Algebra: Chapters 1-7

Integration II: Chapters 7–9 (Elements of Mathematics)