000 03524nam a22004815i 4500
001 978-3-540-31546-9
003 DE-He213
005 20190213151746.0
007 cr nn 008mamaa
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020 _a9783540315469
_9978-3-540-31546-9
024 7 _a10.1007/11551621
_2doi
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
_2thema
082 0 4 _a515.7
_223
100 1 _aGurariy, Vladimir I.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aGeometry of Müntz Spaces and Related Questions
_h[electronic resource] /
_cby Vladimir I. Gurariy, Wolfgang Lusky.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2005.
300 _aXIII, 176 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1870
505 0 _aPreface -- 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.
520 _aStarting 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.
650 0 _aFunctional analysis.
650 0 _aGeometry.
650 1 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aGeometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21006
700 1 _aLusky, Wolfgang.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540815419
776 0 8 _iPrinted edition:
_z9783540288008
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1870
856 4 0 _uhttps://doi.org/10.1007/11551621
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11787
_d11787