LEADER 03492nam 2200601 450 001 996466522503316 005 20220212093855.0 010 $a3-540-31546-2 024 7 $a10.1007/11551621 035 $a(CKB)1000000000232560 035 $a(DE-He213)978-3-540-31546-9 035 $a(SSID)ssj0000317945 035 $a(PQKBManifestationID)11205736 035 $a(PQKBTitleCode)TC0000317945 035 $a(PQKBWorkID)10308485 035 $a(PQKB)10676646 035 $a(MiAaPQ)EBC4976143 035 $a(Au-PeEL)EBL4976143 035 $a(CaONFJC)MIL140415 035 $a(OCoLC)1024284003 035 $a(MiAaPQ)EBC6866473 035 $a(Au-PeEL)EBL6866473 035 $a(PPN)123097371 035 $a(EXLCZ)991000000000232560 100 $a20220212d2005 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometry of muentz spaces and related questions /$fVladimir Gurariy, Wolfgang Lusky 205 $a1st ed. 2005. 210 1$aBerlin :$cSpringer,$d[2005] 210 4$d©2005 215 $a1 online resource (XIII, 176 p.) 225 1 $aLecture notes in mathematics ;$v1870 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-28800-7 327 $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. 330 $aStarting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The resulting spaces of Muentz polynomials are largely unexplored as far as the Banach space geometry is concerned and deserve the attention that the authors arouse. They present the known theorems and prove new results concerning, for example, the isomorphic and isometric classification and the existence of bases in these spaces. Moreover they state many open problems. Although the viewpoint is that of the geometry of Banach spaces they only assume that the reader is familiar with basic functional analysis. In the first part of the book the Banach spaces notions are systematically introduced and are later on applied for Muentz spaces. They include the opening and inclination of subspaces, bases and bounded approximation properties and versions of universality. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1870. 606 $aFunctional analysis 615 0$aFunctional analysis. 676 $a515.7 700 $aGurariy$b Vladimir I.$0472493 702 $aLusky$b Wolfgang$f1948- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466522503316 996 $aGeometry of muentz spaces and related questions$92597311 997 $aUNISA