000			03829nam a22004695i 4500
001			978-3-7643-7360-3
003			DE-He213
005			20160302161912.0
007			cr nn 008mamaa
008			100301s2005 sz | s |||| 0|eng d
020			_a9783764373603 _9978-3-7643-7360-3
024	7		_a10.1007/3-7643-7360-1 _2doi
050		4	_aQA319-329.9
072		7	_aPBKF _2bicssc
072		7	_aMAT037000 _2bisacsh
082	0	4	_a515.7 _223
100	1		_aArgyros, Spiros A. _eauthor.
245	1	0	_aRamsey Methods in Analysis _h[electronic resource] / _cby Spiros A. Argyros, Stevo Todorcevic.
264		1	_aBasel : _bBirkh�user Basel, _c2005.
300			_aVI, 257 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aAdvanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matem�tica
505	0		_aSaturated 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 Hereditarily Indecomposable Banach Spaces -- Examples of Hereditarily Indecomposable Extensions -- The Space $$\mathfrak{X}\omega _1 $$ -- The Finite Representability of $$J_{T_0 }$$ and the Diagonal Space $$D \left( {\mathfrak{X}_\gamma } \right)$$ -- The Spaces of Operators $$L\left( {\mathfrak{X}_\gamma } \right)$$ , $$L\left( {X,\mathfrak{X}\omega _1 } \right)$$ -- Transfinite Schauder Basic Sequences -- The Proof of the Finite Representability of $$J_{T_0 }$$ -- High-Dimensional Ramsey Theory and Banach Space Geometry -- Finite-Dimensional Ramsey Theory: Finite Representability of Banach Spaces -- Ramsey Theory of Finite and Infinite Sequences -- Ramsey Theory of Finite and Infinite Block Sequences -- Approximate and Strategic Ramsey Theory of Banach Spaces.
520			_aThis 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.
650		0	_aMathematics.
650		0	_aFunctional analysis.
650		0	_aCombinatorics.
650	1	4	_aMathematics.
650	2	4	_aFunctional Analysis.
650	2	4	_aCombinatorics.
700	1		_aTodorcevic, Stevo. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783764372644
830		0	_aAdvanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matem�tica
856	4	0	_uhttp://dx.doi.org/10.1007/3-7643-7360-1
912			_aZDB-2-SMA
999			_c174849 _d174849