TY - BOOK ID - 209486 TI - Ramsey Methods in Analysis AU - Argyros, Spiros A. AU - Todorcevic, Stevo. PY - 2005 SN - 3764373601 3764372648 PB - Basel : Birkhäuser Basel : Imprint: Birkhäuser, DB - UniCat KW - Normed linear spaces. KW - Ramsey theory. KW - Set theory. KW - Aggregates KW - Classes (Mathematics) KW - Ensembles (Mathematics) KW - Mathematical sets KW - Sets (Mathematics) KW - Theory of sets KW - Logic, Symbolic and mathematical KW - Mathematics KW - Combinatorial analysis KW - Graph theory KW - Linear normed spaces KW - Normed vector spaces KW - Banach spaces KW - Functional analysis KW - Vector analysis KW - Functional analysis. KW - Combinatorics. KW - Functional Analysis. KW - Functional calculus KW - Calculus of variations KW - Functional equations KW - Integral equations KW - Combinatorics KW - Algebra KW - Mathematical analysis KW - Combinatorial analysis. UR - https://www.unicat.be/uniCat?func=search&query=sysid:209486 AB - This book introduces graduate students and resarchers 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. ER -