E-Locus - Institutional Repository of the University of Crete

Home Collections School/Department School of Sciences and Engineering Department of Mathematics and Applied Mathematics Post-graduate theses

Post-graduate theses

Current Record: 91 of 127

[Add to Basket]

Identifier

000410113

Title

Το πρόβλημα της προσέγγισης σε χώρους Banach

Alternative Title

The problem of aproximation property in Banach spaces

Author

Ηλιάκης, Αντώνιος Ελευθέριος

Thesis advisor

Καμβύσης, Σπυρίδων

Abstract

In this work, we will present the counterexample of Per Enflo for the approximation property problem in Banach spaces, which was formulated by Stanislaw Mazur at 1936. Specifically, we will construct a reflexive separable Banach space which will have neither the approximation property nor the bounded approximation property. Also we will see that the space has no a Schauder basis. In order to do this, we will prove a theorem according to which the space that will fulfill these assumptions will not have the bounded aproximation property. By defining finiteexpansion operators with a finite trace, we will prove some propositions that are associated to this central theorem. Its construction is described particularly in the third chapter of this work and is the result of an extremely subtle combination of the walsh functions are defined in the second chapter. Finally, we will ensure that the space we have constructed satisfies the assumptions of the theorem and thus we end up with the desired result.

Language

Greek

Subject

Functional analysis

Συναρτησιακή ανάλυση

Issue date

2017-07-21

Collection

School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses

Type of Work--Post-graduate theses

Permanent Link

https://elocus.lib.uoc.gr//dlib/d/3/4/metadata-dlib-1500637076-712327-9911.tkl