The Resource Ramsey methods in analysis, Spiros A. Argyros, Stevo Todorcevic

# Ramsey methods in analysis, Spiros A. Argyros, Stevo Todorcevic Resource Information The item Ramsey methods in analysis, Spiros A. Argyros, Stevo Todorcevic represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.

Label
Ramsey methods in analysis
Title
Ramsey methods in analysis
Statement of responsibility
Spiros A. Argyros, Stevo Todorcevic
Creator
Contributor
Subject
Language
eng
Summary
"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
Member of
COO
1950-
Argyros, S.
Dewey number
515/.732
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA322.2
LC item number
.A74 2005
Literary form
non fiction
Nature of contents
• dictionaries
• bibliography
Todorcevic, Stevo
Series statement
Advanced courses in mathematics, CRM Barcelona
• Normed linear spaces
• Ramsey theory
• Set theory
• 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
Label
Ramsey methods in analysis, Spiros A. Argyros, Stevo Todorcevic
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 247-252) and index
Carrier category
online resource
Carrier category code
• cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
• txt
Content type MARC source
rdacontent
Contents
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 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
Control code
288229504
Dimensions
unknown
Extent
1 online resource (257 pages)
Form of item
online
Isbn
9783764373603
Media category
computer
Media MARC source
rdamedia
Media type code
• c
Other control number
10.1007/3-7643-7360-1
Other physical details
illustrations.
134924
Specific material designation
remote
System control number
(OCoLC)288229504
Label
Ramsey methods in analysis, Spiros A. Argyros, Stevo Todorcevic
Publication
Bibliography note
Includes bibliographical references (pages 247-252) and index
Carrier category
online resource
Carrier category code
• cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
• txt
Content type MARC source
rdacontent
Contents
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 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
Control code
288229504
Dimensions
unknown
Extent
1 online resource (257 pages)
Form of item
online
Isbn
9783764373603
Media category
computer
Media MARC source
rdamedia
Media type code
• c
Other control number
10.1007/3-7643-7360-1
Other physical details
illustrations.
134924
Specific material designation
remote
System control number
(OCoLC)288229504

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