About: Tsirelson space

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In mathematics, especially in functional analysis, the Tsirelson space is the first example of a Banach space in which neither an ℓ p space nor a c0 space can be embedded. The Tsirelson space is reflexive.

Attributes	Values
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rdfs:label	Tsirelson space (en)
rdfs:comment	In mathematics, especially in functional analysis, the Tsirelson space is the first example of a Banach space in which neither an ℓ p space nor a c0 space can be embedded. The Tsirelson space is reflexive. (en)
dcterms:subject	Banach spaces
Wikipage page ID	628352 (xsd:integer)
Wikipage revision ID	1039415036 (xsd:integer)
Link from a Wikipage to another Wikipage	Product topology Approximation property Banach spaces James' space Compact space Continuous function Mathematics Separable space Convex hull Linear operator Lp space Functional analysis Schauder basis Banach space Timothy Gowers Weak topology Distortion problem Israel Journal of Mathematics Pointwise convergence Isomorphic Banach-Mazur compactum Advances in Mathematics Differentiable function Metrization theorem Ordinal number Reflexive space Sequence space Unit vector Unit ball Polynomially reflexive space Uncountable B. S. Tsirelson Integrable function dbr:Finitely_universal_space
Link from a Wikipage to an external page	http://www.tau.ac.il/~tsirel/Research/myspace/remins.html http://www.numdam.org/item%3Fid=CM_1974__29_2_179_0
sameAs	Tsirelson space Tsirelson space Tsirelson space Tsirelson space
dbp:wikiPageUsesTemplate	dbt:= dbt:Citation dbt:Harvtxt dbt:Mvar dbt:Reflist dbt:Functional_analysis dbt:Banach_Théorie_des_Opérations_Linéaires
has abstract	In mathematics, especially in functional analysis, the Tsirelson space is the first example of a Banach space in which neither an ℓ p space nor a c0 space can be embedded. The Tsirelson space is reflexive. It was introduced by B. S. Tsirelson in 1974. The same year, Figiel and Johnson published a related article where they used the notation T for the dual of Tsirelson's example. Today, the letter T is the standard notation for the dual of the original example, while the original Tsirelson example is denoted by T. In T or in T, no subspace is isomorphic, as Banach space, to an ℓ p space, 1 ≤ p < ∞, or to c0. All classical Banach spaces known to , spaces of continuous functions, of differentiable functions or of integrable functions, and all the Banach spaces used in functional analysis for the next forty years, contain some ℓ p or c0. Also, new attempts in the early '70s to promote a geometric theory of Banach spaces led to ask whether or not every infinite-dimensional Banach space has a subspace isomorphic to some ℓ p or to c0. The radically new Tsirelson construction is at the root of several further developments in Banach space theory: the arbitrarily distortable space of Schlumprecht, on which depend Gowers' solution to Banach's hyperplane problem and the Odell–Schlumprecht solution to the distortion problem. Also, several results of Argyros et al. are based on ordinal refinements of the Tsirelson construction, culminating with the solution by Argyros–Haydon of the scalar plus compact problem. (en)
gold:hypernym	Example
prov:wasDerivedFrom	wikipedia-en:Tsirelson_space?oldid=1039415036&ns=0
page length (characters) of wiki page	13007 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Tsirelson_space
is Link from a Wikipage to another Wikipage of	List of functional analysis topics Boris Tsirelson Approximation property James' space List of mathematical examples Distortion problem List of Banach spaces Sequence space List of vector spaces in mathematics Polynomially reflexive space
is known for of	Boris Tsirelson
is known for of	Boris Tsirelson
is foaf:primaryTopic of	wikipedia-en:Tsirelson_space

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