03492nam 2200601 450 99646652250331620220212093855.03-540-31546-210.1007/11551621(CKB)1000000000232560(DE-He213)978-3-540-31546-9(SSID)ssj0000317945(PQKBManifestationID)11205736(PQKBTitleCode)TC0000317945(PQKBWorkID)10308485(PQKB)10676646(MiAaPQ)EBC4976143(Au-PeEL)EBL4976143(CaONFJC)MIL140415(OCoLC)1024284003(MiAaPQ)EBC6866473(Au-PeEL)EBL6866473(PPN)123097371(EXLCZ)99100000000023256020220212d2005 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierGeometry of muentz spaces and related questions /Vladimir Gurariy, Wolfgang Lusky1st ed. 2005.Berlin :Springer,[2005]©20051 online resource (XIII, 176 p.) Lecture notes in mathematics ;1870Bibliographic Level Mode of Issuance: Monograph3-540-28800-7 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.Lecture notes in mathematics (Springer-Verlag) ;1870.Functional analysisFunctional analysis.515.7Gurariy Vladimir I.472493Lusky Wolfgang1948-MiAaPQMiAaPQMiAaPQBOOK996466522503316Geometry of muentz spaces and related questions2597311UNISA