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Reference: Derrick, John, (1988). Some problems in Banach space theory. DPhil. University of Oxford.Citable link to this page:

 

Some problems in Banach space theory

Abstract: Types were introduced by Krivine and Maurey, in arefinement of a result by Aldous showing that infinitedimensional subspaces of Lr contain Ωp for some 1≤pꝏ) . Asynthesis of these ideas was provided by Garling whoserepresentation of types as random measures was the motivationfor much of this work. This thesis aims to investigate thestructure of the representation, and to provide concreterepresentations for differing Banach spaces.Chapter one contains the necessary preliminaries for thelater chapters, and finishes by introducing therepresentation due to Garling of types on Lϕ(X) as randommeasures on 𝒯(X)The second chapter consists of two parts. In the firstpart we examine the structure of the map between types onLp(X) and random measures on 𝒯(X) . We show that convolutionis preserved by the mapping, and give an explicitrepresentation of the space of types on L1(Ωp). The secondpart is concerned with representations of 𝒯(X) . We giveconditions for the decomposition of 𝒯(X) into X*𝒮(X) , andderive representations for the space of types on L1(L2k).The third chapter studies differentiability of types. Weextend differentiability from X to 𝒯(X) , and develop ideasthat will be used in the study of uniqueness.In chapter four we consider questions concerning theuniqueness of measures and random measures on X and 𝒯(X) . Weconstruct spaces where the representation of types as randommeasures is not in uniquely determined. We prove that if acertain uniqueness property for measures on X fails then Ωn1embeds in X.

Type of Award:DPhil Level of Award:Doctoral Awarding Institution: University of Oxford Notes:This thesis was digitised thanks to the generosity of Dr Leonard Polonsky

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Haydon, R. (Richard)More by this contributor

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Dr. R. G. HaydonMore by this contributor

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 Bibliographic Details

Issue Date: 1988Identifiers

Urn: uuid:36289504-6d9f-42e4-af95-ef3abb8a8fa2

Source identifier: 602835276 Item Description

Type: Thesis;

Language: eng Subjects: Banach spaces Tiny URL: td:602835276

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Author: Derrick, John - institutionUniversity of Oxford facultyMathematical and Physical Sciences Division - - - - Contributors Haydon, R

Source: https://ora.ox.ac.uk/objects/uuid:36289504-6d9f-42e4-af95-ef3abb8a8fa2



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