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Convergence Structures and Applications to Functional Analysis: Convergence Structures and Applications to Functional Analysis - Brossura
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This text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of functional analysis. While there are a few books dealing with convergence spaces and a great many on functional analysis, there are none with this particular focus.
The book demonstrates the applicability of convergence structures to functional analysis. Highlighted here is the role of continuous convergence, a convergence structure particularly appropriate to function spaces. It is shown to provide an excellent dual structure for both topological groups and topological vector spaces.
Readers will find the text rich in examples. Of interest, as well, are the many filter and ultrafilter proofs which often provide a fresh perspective on a well-known result.
Audience: This text will be of interest to researchers in functional analysis, analysis and topology as well as anyone already working with convergence spaces. It is appropriate for senior undergraduate or graduate level students with some background in analysis and topology.
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Contenuti
Introduction. 1. Convergence spaces. 2. Uniform convergence spaces. 3. Convergence vector spaces. 4. Duality. 5. Hahn-Banach extension theorems. 6. The closed graph theorem. 7. The Banach-Steinhaus theorem. 8. Duality theory for convergence groups. Bibliography. List of Notations. Index
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Convergence Structures and Applications to Functional Analysis
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Convergence Structures and Applications to Functional Analysis
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Convergence Structures and Applications to Functional Analysis
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Springer Netherlands Dez 2010, 2010
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ISBN 13: 9789048159949
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -For many, modern functional analysis dates back to Banach's book [Ba32]. Here, such powerful results as the Hahn-Banach theorem, the open-mapping theorem and the uniform boundedness principle were developed in the setting of complete normed and complete metrizable spaces. When analysts realized the power and applicability of these methods, they sought to generalize the concept of a metric space and to broaden the scope of these theorems. Topological methods had been generally available since the appearance of Hausdorff's book in 1914. So it is surprising that it took so long to recognize that they could provide the means for this generalization. Indeed, the theory of topo logical vector spaces was developed systematically only after 1950 by a great many different people, induding Bourbaki, Dieudonne, Grothendieck, Köthe, Mackey, Schwartz and Treves. The resulting body of work produced a whole new area of mathematics and generalized Banach's results. One of the great successes here was the development of the theory of distributions. While the not ion of a convergent sequence is very old, that of a convergent fil ter dates back only to Cartan [Ca]. And while sequential convergence structures date back to Frechet [Fr], filter convergence structures are much more recent: [Ch], [Ko] and [Fi]. Initially, convergence spaces and convergence vector spaces were used by [Ko], [Wl], [Ba], [Ke64], [Ke65], [Ke74], [FB] and in particular [Bz] for topology and analysis. 280 pp. Englisch. Codice articolo 9789048159949
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Convergence Structures and Applications to Functional Analysis: Convergence Structures and Applications to Functional Analysis
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Convergence Structures and Applications to Analysis. Proceedings of the International Summer School held at Frankfurt from may 8 to 12, 1978
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Akademie-Verlag Nr. 4 N, 1980
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ISBN 13: 9789048159949
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Condizione: Gut - gebraucht. Broschiert Guter Zustand Zustand: 3, Gut - gebraucht, Broschiert Akademie-Verlag Nr. 4 N , 1980 , Convergence Structures and Applications to Analysis. Proceedings of the International Summer School held at Frankfurt from may 8 to 12, 1978, S. Gähler, W. Gähler, G. Kneis. Codice articolo BU363266
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Introduction. 1. Convergence spaces. 2. Uniform convergence spaces. 3. Convergence vector spaces. 4. Duality. 5. Hahn-Banach extension theorems. 6. The closed graph theorem. 7. The Banach-Steinhaus theorem. 8. Duality theory for convergence groups. Bibl. Codice articolo 5819847
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Convergence Structures and Applications to Functional Analysis
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Condizione: New. PRINT ON DEMAND pp. 280. Codice articolo 183060124
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