ENGLISH

Geometry of Müntz Spaces and Related Questions

By Vladimir I. Gurariy , Wolfgang Lusky (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2005
ISBN
9783540288008, 3540288007
DOI
10.1007/11551621
ISSN
0075-8434
Open Library ID
OL9055918M
Language
english
Format
PDF
Filesize
1 MB (1414729 bytes)
Series
Lecture Notes in Mathematics 1870
Edition
1
Pages
176\186
Time added
2009-08-06 05:14:26
Functional Analysis; Geometry

Description

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.

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