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＜電子ブック＞
Tsirelson's Space / by Peter G. Casazza, Thaddeus J. Shura
(Lecture Notes in Mathematics. ISSN:16179692 ; 1363)

版	1st ed. 1989.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1989
大きさ	X, 206 p : online resource
著者標目	*Casazza, Peter G author Shura, Thaddeus J author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis FREE:Analysis
一般注記	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 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) HTTP:URL=https://doi.org/10.1007/BFb0085267

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