Tsirelson's Space : With an Appendix by J. Baker, O. Slotterbeck and R. Aron

This Monograph Provides A Structure Theory For The Increasingly Important Banach Space Discovered By B.s. Tsirelson. The Basic Construction Should Be Accessible To Graduate Students Of Functional Analysis With A Knowledge Of The Theory Of Schauder Bases, While Topics Of A More Advanced Nature Are Presented For The Specialist. Bounded Linear Operators Are Studied Through The Use Of Finite-dimensional Decompositions, And Complemented Subspaces Are Studied At Length. A Myriad Of Variant Constructions Are Presented And Explored, While Open Questions Are Broached In Almost Every Chapter. Two Appendices Are Attached: One Dealing With A Computer Program Which Computes Norms Of Finitely-supported Vectors, While The Other Surveys Recent Work On Weak Hilbert Spaces (where A Tsirelson-type Space Provides An Example). Contents: Precursors Of The Tsirelson Construction -- The Figiel-johnson Construction Of Tsirelson's Space -- Block Basic Sequences In Tsirelson's Space -- Bounded Linear Operators On T And The Blocking Principle -- Subsequences Of The Unit Vector Basis Of Tsirelson's Space -- Modified Tsirelson's Space: Tm -- Embedding Theorems About T And T* -- Isomorphisms Between Subspaces Of Tsirelson's Space Which Are Spanned By Subsequences ätn ü -- Permutations Of The Unit Vector Basis Of Tsirelson's Space -- Unconditional Bases For Complemented Subspaces Of Tsirelson's Space -- Variations On A Theme -- Some Final Comments -- Appendices -- Index. Peter G. Casazza, Thaddeus J. Shura ; With An Appendix By J. Baker, O. Slotterbeck, And R. Aron. Includes Index. Includes Bibliographical References And Index. Precursors of the Tsirelson construction....Pages 1-7 The Figiel-Johnson construction of Tsirelson's space....Pages 8-18 Block basic sequences in Tsirelson's space....Pages 19-23 Bounded linear operators on T and the “blocking” principle....Pages 24-34 Subsequences of the unit vector basis of Tsirelson's space....Pages 35-47 Modified Tsirelson's Space: T M ....Pages 48-53 Embedding Theorems about T and T....Pages 54-59 Isomorphisms between subspaces of Tsirelson's space which are spanned by subsequences of $$\left\{ {t_n } \right\}_{n = 1}^\infty$$ ....Pages 60-66 Permutations of the unit vector basis of Tsirelson's space....Pages 67-81 Unconditional bases for complemented subspaces of Tsirelson's space....Pages 82-94 Variations on a Theme....Pages 95-118 Some final comments....Pages 119-120