Post-graduate theses
Current Record: 91 of 127
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Identifier |
000410113 |
Title |
Το πρόβλημα της προσέγγισης σε χώρους Banach |
Alternative Title |
The problem of aproximation property in Banach spaces |
Author
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Ηλιάκης, Αντώνιος Ελευθέριος
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Thesis advisor
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Καμβύσης, Σπυρίδων
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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.
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Language |
Greek |
Subject |
Functional analysis |
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Συναρτησιακή ανάλυση |
Issue date |
2017-07-21 |
Collection
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School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
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Type of Work--Post-graduate theses
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Permanent Link |
https://elocus.lib.uoc.gr//dlib/d/3/4/metadata-dlib-1500637076-712327-9911.tkl
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Views |
486 |