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＜電子ブック＞
Geometry of Müntz Spaces and Related Questions / by Vladimir I. Gurariy, Wolfgang Lusky
(Lecture Notes in Mathematics. ISSN:16179692 ; 1870)

版	1st ed. 2005.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2005
本文言語	英語
大きさ	XIII, 176 p : online resource
著者標目	*Gurariy, Vladimir I author Lusky, Wolfgang author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Geometry FREE:Functional Analysis FREE:Geometry
一般注記	Preface -- Part I Subspaces and Sequences in Banach Spaces: Disposition of Subspaces -- Sequences in Normed Spaces -- Isomorphism, Isometries and Embeddings -- Spaces of Universal Disposition -- Bounded Approximation Properties -- Part II On the Geometry of Müntz Sequences: Coefficient Estimates and the Müntz Theorem -- Classification and Elementary Properties of Müntz Sequences -- More on the Geometry of Müntz Sequences and Müntz Polynomials -- Operators of Finite Rank and Bases in Müntz Spaces -- Projection Types and the Isomorphism Problem for Müntz Spaces -- The Classes [M], A, P, and Pe -- Finite Dimensional Müntz Limiting Spaces in C -- References -- Index Starting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The resulting spaces of Muentz polynomials are largely unexplored as far as the Banach space geometry is concerned and deserve the attention that the authors arouse. They present the known theorems and prove new results concerning, for example, the isomorphic and isometric classification and the existence of bases in these spaces. Moreover they state many open problems. Although the viewpoint is that of the geometry of Banach spaces they only assume that the reader is familiar with basic functional analysis. In the first part of the book the Banach spaces notions are systematically introduced and are later on applied for Muentz spaces. They include the opening and inclination of subspaces, bases and bounded approximation properties and versions of universality HTTP:URL=https://doi.org/10.1007/11551621

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