Topics in Banach Space Theory. 2nd ed. 2016

種類:

電子ブック

責任表示:

by Fernando Albiac, Nigel J. Kalton

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2016

著者名:

• Albiac, Fernando.
• Kalton, Nigel J.
• SpringerLink (Online service)

シリーズ名:

Graduate Texts in Mathematics ; 233

ISBN:

9783319315577 [3319315579]    

注記:

1. Bases and Basic Sequences -- 2. The Classical Sequence Spaces -- 3. Special Types of Bases -- 4. Banach Spaces of Continuous Functions -- 5. L_{1}(¥mu )-Spaces and ¥mathcal C(K)-Spaces -- 6. The Spaces L_{p} for 1¥le p^I Basic probability in use -- Appendix J Generalities on Ultraproducts -- Appendix K The Bochner Integral abridged -- List of Symbols -- References -- Index.
This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous f

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