Unit:
Τομέας Μαθηματικής ΑνάλυσηςLibrary of the School of Science
Author:
Γλακουσάκης Ευτύχιος
Supervisors info:
Σ. Μερκουράκης Καθηγητής (επιβλέπων), Γ. Κουμουλλής Καθηγητής, Α. Τσαρπαλιάς Καθηγητής ,
Original Title:
Διαχωρισμένες ακολουθίες σε απειροδιάστατους χώρους με νόρμα-το Θεώρημα Elton-Odell
Summary:
The purpose of this dissertation is to illustrate the presence of separated
sequences and spreading models with appropriate properties in infinite Banach
spaces. This was achieved by utilising methods from Ramsey theory. In the first
chapter, the proof of Kottman’s theorem is being provided, that “Every infinite
Banach space includes a normalised sequence separated by more than one”.
Moreover, it is proven that if a Banach space X contains an isomorphic copy of
any of the classical Banach spaces c0 or lp , 1p<,then it also includes a
normalised 1+ε- separated sequence. This stronger last result has also been
proven in the non reflexive Banach spaces case by Kryczka and Prus. The second
chapter is dedicated in the proof of the Elton-Odell theorem, that “Every
infinite Banach space includes a normalised 1+ε- separated sequence”. In the
last chapter, the following Rosenthal result is being proven that “Every
infinite Banach space has an 1-inconditional spreading model”.
Keywords:
Elton, Odell, Spreading models, Separated sequences, Unconditional
Number of index pages:
iii
