An introduction to nuclear space



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Bessaga, C. and Hernando Boto, Beatriz and Martín Peinador, Elena (1997) An introduction to nuclear space. Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, 9 . pp. 1-48. ISSN 1132-6360

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This is a small book (48 pages) that contains a revised and extended version of the notes of seminar lectures given by Bessaga. The authors present a nice introduction to nuclear spaces (with all necessary preliminaries) based on Kolmogorov diameters. They consider only some of the most important topics of the theory of nuclear spaces, namely Kolmogorov diameters, nuclear operators, Mityagin's characterization of nuclear spaces, the theorem on absoluteness of bases in nuclear spaces, the uniqueness problem for bases (together with the theorem on quasiequivalence of regular bases), examples of nuclear Fréchet spaces without basis. Of course, many of the important topics in the theory of nuclear spaces are not even touched. Nevertheless, this book may be recommended to anyone who wants to study nuclear spaces, since it is practically independent of other sources and covers an essential part of the theory. Moreover, the authors do their best to help the reader: the proofs of all theorems are complete and the organization of the material is perfect.

Item Type:Article
Uncontrolled Keywords:Nuclear operators; Mitiagin's characterization; regular bases; nuclear Fréchet space; nuclear spaces; Kolmogorov diameters; Kolmogorov numbers
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:22295
Deposited On:09 Jul 2013 17:23
Last Modified:12 Dec 2018 15:13

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