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＜電子ブック＞
Open Problems in the Geometry and Analysis of Banach Spaces / by Antonio J. Guirao, Vicente Montesinos, Václav Zizler

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
本文言語	英語
大きさ	XII, 169 p. 1 illus : online resource
著者標目	*Guirao, Antonio J author Montesinos, Vicente author Zizler, Václav author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Approximation theory LCSH:Measure theory LCSH:Convex geometry  LCSH:Discrete geometry LCSH:Algebraic topology FREE:Functional Analysis FREE:Approximations and Expansions FREE:Measure and Integration FREE:Convex and Discrete Geometry FREE:Algebraic Topology
一般注記	Preface -- Basic linear structure -- Basic linear geometry -- Biorthogonal systems -- Smoothness, smooth approximation -- Nonlinear geometry -- Some more nonseparable problems -- Some applications -- Bibliography -- List of concepts and problems -- Symbol index -- Subject index. This is a collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help convince young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems presented herein are longstanding open problems, some arerecent, some are more important and some are only "local" problems. Some would require new ideas, while others may be resolved with only a subtle combination of known facts. Regardless of their origin or longevity, each of these problems documents the need for further research in this area HTTP:URL=https://doi.org/10.1007/978-3-319-33572-8

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