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.
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.
- 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
- Language
- eng
- Extent
- 1 online resource (257 pages)
- 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
- Isbn
- 9783764373603
- Label
- Ramsey methods in analysis
- Title
- Ramsey methods in analysis
- Statement of responsibility
- Spiros A. Argyros, Stevo Todorcevic
- 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
- Cataloging source
- COO
- http://library.link/vocab/creatorDate
- 1950-
- http://library.link/vocab/creatorName
- 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
- http://library.link/vocab/relatedWorkOrContributorName
- Todorcevic, Stevo
- Series statement
- Advanced courses in mathematics, CRM Barcelona
- http://library.link/vocab/subjectName
-
- 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
- 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.
- http://library.link/vocab/ext/overdrive/overdriveId
- 134924
- Specific material designation
- remote
- System control number
- (OCoLC)288229504
- Label
- Ramsey methods in analysis, Spiros A. Argyros, Stevo Todorcevic
- 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.
- http://library.link/vocab/ext/overdrive/overdriveId
- 134924
- Specific material designation
- remote
- System control number
- (OCoLC)288229504
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Ramsey-methods-in-analysis-Spiros-A.-Argyros/DQlNC2bUB6g/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Ramsey-methods-in-analysis-Spiros-A.-Argyros/DQlNC2bUB6g/">Ramsey methods in analysis, Spiros A. Argyros, Stevo Todorcevic</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
