Descripción del título
Ramsey methods in analysis ...
"This book introduces graduate students and researchers to the study of the geometry of Banach spaces using combinatorial methods. The combinatorial, and in particular the Ramsey-theoretic, approach to Banach space theory is not new; it can be traced back as early as the 1970s. Its full appreciation, however, came only during the last decade or so, after some of the most important problems in Banach space theory were solved, such as, for example, the distortion problem, the unconditional basic sequence problem, and the homogeneous space problem. The book covers most of these advances, but one of its primary purposes is to discuss some of the recent advances that are not present in survey articles of these areas. We show, for example, how to introduce a conditional structure to a given Banach space under construction that allows us to essentially prescribe the corresponding space of non-strictly singular operators. We also apply the Nash-Williams theory of fronts and barriers in the study of Cezaro summability and unconditionality present in basic sequences inside a given Banach space. We further provide a detailed exposition of the block-Ramsey theory and its recent deep adjustments relevant to the Banach space theory due to Gowers."--Jacket
Monografía
monografia Rebiun34257000 https://catalogo.rebiun.org/rebiun/record/Rebiun34257000 m o d cr |n||||||||| 050427s2005 sz a ob 001 0 eng c 2005048011 209873475 646746279 690009912 696922926 698463248 739128293 756421201 880023923 911079181 985041617 990406926 1005748358 1035703523 1044249955 1044308479 1056363999 1056397041 1077228510 1087301998 1097267031 1097353512 1102298793 1110948895 1110988621 1112599530 1153016130 1204022955 1391802459 0817672648 alk. paper) 9780817672645 alk. paper) 3764372648 alk. paper) 9783764372644 alk. paper) 9783764373603 3764373601 1281349240 9781281349248 10.1007/3-7643-7360-1 doi AU@ 000042137339 DEBSZ 264363574 DKDLA 820120-katalog:000662944 NLGGC 384202837 NZ1 12054717 134924 MIL COO eng pn COO NUI DKU E7B OCLCQ GW5XE YNG OCLCO A7U OCLCQ OCLCF AZU YDXCP SLY OCLCQ DEBSZ IDEBK VT2 Z5A LIP OCLCQ UAB ESU OCLCQ STF OCLCQ U3W OCLCQ WYU CEF ICG YOU W2U CNTRU AUD OCLCQ ZHM DCT ERF OCLCQ OCLCO OCLCQ IND pcc QA lcco PBKF bicssc MAT037000 bisacsh 515/.732 22 31.46 bcl O177. 2 clc Argyros, S. Spiros) 1950-) Ramsey methods in analysis Spiros A. Argyros, Stevo Todorcevic Basel Boston Birkhäuser 2005 Basel Boston Basel Boston Birkhäuser 1 online resource (257 pages) illustrations 1 online resource (257 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF Advanced courses in mathematics, CRM Barcelona Includes bibliographical references (pages 247-252) and index A saturated and conditional structures in banach spaces -- Tsirelson and mixed Tsirelson spaces -- Tree complete extensions of a ground norm -- Hereditarily indecomposable extensions with a Schauder basis -- The space of the operators for HI Banach spaces -- Examples of hereditary indecomposable extensions -- The space -- Finite represent ability of and the diagonal space -- The space of operators -- High-dimensional Ramsey theory and Banach space geometry -- Finite-dimensional Ramsey theory -- Ramsey theory of finite and infinite sequences -- Ramsey theory of finite and infinite block sequences -- Approximate and strategic Ramsey theory of Banach spaces University staff and students only. Requires University Computer Account login off-campus "This book introduces graduate students and researchers to the study of the geometry of Banach spaces using combinatorial methods. The combinatorial, and in particular the Ramsey-theoretic, approach to Banach space theory is not new; it can be traced back as early as the 1970s. Its full appreciation, however, came only during the last decade or so, after some of the most important problems in Banach space theory were solved, such as, for example, the distortion problem, the unconditional basic sequence problem, and the homogeneous space problem. The book covers most of these advances, but one of its primary purposes is to discuss some of the recent advances that are not present in survey articles of these areas. We show, for example, how to introduce a conditional structure to a given Banach space under construction that allows us to essentially prescribe the corresponding space of non-strictly singular operators. We also apply the Nash-Williams theory of fronts and barriers in the study of Cezaro summability and unconditionality present in basic sequences inside a given Banach space. We further provide a detailed exposition of the block-Ramsey theory and its recent deep adjustments relevant to the Banach space theory due to Gowers."--Jacket English Normed linear spaces Ramsey theory Set theory Espaces linéaires normés Théorie de Ramsey Théorie des ensembles Ramsey theory Set theory Geometria de espaços de banach Análise funcional Normed linear spaces Normed linear spaces Ramsey theory Set theory Geometria de espaços de banach Análise funcional Todorcevic, Stevo Springer eBooks Springer eBooks Print version Argyros, S. (Spiros), 1950-. Ramsey methods in analysis. Basel ; Boston : Birkhäuser, 2005 (DLC) 2005048011 Advanced courses in mathematics, CRM Barcelona