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2009 (EN)
The Tsirelson space
Ο χώρος του Τσίρελσον

Μυργιώτης, Απόστολος Παναγιώτη

The Tsirelson space consists of sequences, has infinite dimwnsions, is Banach and reflexive. Also, is proved that (Co, || ||∞) and (lp, || ||p), ∀p∈[1, +∞) are not contained isomorphically in Tsirelson space. The last property makes Tsirelson space important because answers negatively in a conjecture in area of Functional Analysis: "Every infinite-dimension and reflexive Banach space contains isomorphically (Co, || ||∞) or (lp, || ||p), for p∈[1, +∞)
Ο χώρος του Tsirelson είναι ένας χώρος ακολουθιών, απειροδιάστατος, Banach και αυτοπαθής. Στην εργασία αποδεικνύονται οι παραπάνω ιδιότητες καθώς και το ότι οι χώροι (Co, || ||∞) και (lp, || ||p),∀p∈[1, +∞) δεν εμφυτεύονται ισομορφικά σ' αυτόν. Η τελευταία ιδιότητα τον καθιστά αξιόλογο, επειδή με την κατασκευή του απαντήθηκε αρνητικά μια εικασία στο χώρο της Συναρτησιακής Ανάλυσης : "Κάθε απειροδιάστατος αυτοπαθής χώρος Banach περιέχει ισομορφικά τον Co ή κάποιον lp, p∈[1, +∞).

Postgraduate Thesis / Μεταπτυχιακή Εργασία

Infinite dimension space
Συναρτησιακή ανάλυση
Χώρος ακολουθιών
Χώρος Banach
Functional analysis
Banach space
Reflexive space
Sequence space

Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (EL)
Aristotle University of Thessaloniki (EN)



Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης, Σχολή Θετικών Επιστημών, Τμήμα Μαθηματικών

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