Nuclear Locally Convex Spaces. Translated from the Second German Edition by William H. Ruckle. (= Ergebnisse der Mathematik und ihrer Grenzgebiete; Band 66).

Pietsch, Albrecht:

ISBN 10: 3540056440 / ISBN 13: 9783540056447

Published by Springer, New York / Heidelberg / Berlin, 1972

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IX, 192 S., 3540056440 Sprache: Englisch Gewicht in Gramm: 460 Groß 8°, Bibliotheks-Exemplar (ordnungsgemäß entwidmet) mit leichten Kleberückständen vom Rückenschild, Stempel auf Titel, insgesamt gutes und innen sauberes Exemplar, Seller Inventory # 80513

Bibliographic Details

Title: Nuclear Locally Convex Spaces. Translated ...

Publisher: Springer, New York / Heidelberg / Berlin

Publication Date: 1972

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Synopsis:

VI closely related to finite dimensional locally convex spaces than are normed spaces. In order to present a clear narrative I have omitted exact references to the literature for individual propositions. However, each chapter begins with a short introduction which also contains historical remarks. Deutsche Akademie der vVissenschaften zu Berlin Institut fur Reine Mathematik Albrecht Pietsch Foreword to the Second Edition Since the appearance of the first edition, some important advances have taken place in the theory of nuclear locally convex spaces. Firsts there is the Universality Theorem ofT. and Y. Komura which fully confirms a conjecture of Grothendieck. Also, of particular interest are some new existence theorems for bases in special nuclear locally convex spaces. Recently many authors have dealt with nuclear spaces of functions and distributions. Moreover, further classes of operators have been found which take the place of nuclear or absolutely summing operators in the theory of nuclear locally convex spaces. Unfortunately, there seem to be no new results on diametrai or approximative dimension and isomorphism of nuclear locally convex spaces. Since major changes have not been absolutely necessary I have restricted myself to minor additions. Only the tenth chapter has been substantially altered. Since the universality results no longer depend on the existence of a basis it was necessary to introduce an independent eleventh chapter on universal nuclear locally convex spaces. In the same chapter s-nuclear locally convex spaces are also briefly treated.