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Record Nr. |
UNISA996466651203316 |
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Autore |
Casazza Peter G. <1945-> |
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Titolo |
Tsirelson's space / / Peter G. Casazza and Thaddeus J. Shura |
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Pubbl/distr/stampa |
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Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1989] |
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©1989 |
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ISBN |
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Edizione |
[1st ed. 1989.] |
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Descrizione fisica |
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1 online resource (X, 206 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1363 |
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Disciplina |
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Soggetti |
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Mathematics |
Banach spaces |
Global analysis (Mathematics) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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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 of -- 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. |
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Sommario/riassunto |
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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 |
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