Geometry of Müntz spaces and related questions
著者
書誌事項
Geometry of Müntz spaces and related questions
（Lecture notes in mathematics, 1870）
Springer, c2005
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注記
Includes bibliographical references (p. [163]-169) and index
内容説明・目次
内容説明
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.
目次
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 Muntz Sequences: Coefficient Estimates and the Muntz Theorem.- Classification and Elementary Properties of Muntz Sequences.- More on the Geometry of Muntz Sequences and Muntz Polynomials.- Operators of Finite Rank and Bases in Muntz Spaces.- Projection Types and the Isomorphism Problem for Muntz Spaces.- The Classes [M], A, P, and Pe.- Finite Dimensional Muntz Limiting Spaces in C.- References.- Index.
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